The general problem with Bostrom's argument is that it tries to apply incorrect probabilstic model. It implicitly assumes independence where there is causal connection, therefore arriving to a wrong conclusion. Similarly to conventional reasoning in Doomsday Argument or Sleeping Beauty problems.

For future humans, say in year 3000, to create simulations of year 2025, first actual year 2025 has to happen in the base reality. And then all the next years up to 3000. We know about it very well. Not a single simulation can happen unless an actual reality happens first.

And yet Bostroms models our knowledge about this setting as if we participate in a probability experiment with random sample between many "simulation" outcomes and one "reality" outcome. The inadequacy of such modelling should be obvious. Consider:

There is a bag with a thousand balls. One red and 999 blue. First a red ball is picked from the bag. Then all the blue balls are picked one by one.

and compare it to

There is a bag with a thousand balls. One red and 999 blue. For a thousand iterations a random ball is picked from the bag.

Clearly, the second procedure is very different from the first. The mathematical model that describes it doesn't describe the first at all for exactly the same reasons why Bostrom's model doesn't describe our knowledge state.

It is physically possible to simulate a conscious mind.

... but it's expensive, especially if you have to simulate its environment as well. You have to use a lot of physical resources to run a high-fidelity simulation. It probably takes irreducibly more mass and energy to simulate any given system with close to "full" fidelity than the system itself uses. You can probably get away with less fidelity than that, but nobody has provided any explanation of how much less or why that works.

There are other, more interesting and important ways to use that compute capacity. Nobody sane, human or alien, is going to waste it on running a crapton of simulations.

Also, nobody knows that all the simulated minds wouldn't be p-zombies, because, regardless of innumerable pompous overconfident claims, nobody understands qualia. Nobody can prove that they're not a p-zombie, but do you think you're a p-zombie? And do we care about p-zombies?

The universe is very big, and there are many, many other aliens.

If that's true, and you haven't provided any evidence for it, then those aliens have many, many other things to simulate. The measure of humans among random aliens' simulations is going to be tiny if it's not zero.

Some aliens will run various simulations.

Again, that doesn't imply that they're going to run enough of them for them to dominate the number of subjective experiences out there, or that any of them will be of humans.

Future humans, or human AI successors, if there are any of either, will probably also run "various simulations", but that doesn't mean they're going to dump the kind of vast resources you're demanding into them.

The number of simulations that are "subjectively indistinguishable" from our own experience far outnumbers authentic evolved humans.

Um, no? Because all of the premises you're using to get there are wrong.

(By "subjectively indistinguishable," I mean the simulates can't tell they're in a simulation. )

By that definition, a simulation that bounces frictionless billiard balls around and labels them as humans is "subjectively indistinguishable" from our own, since the billiard balls have no cognition and can't tell anything about anything at all. You need to do more than that to define the kind of simulation you really mean.

However, this argument carries a dramatic, and in my eyes, frightening implication for our existential situation.

There is not much practical advise following from simulation argument. One I heard that we should try to live most interesting lives, so the simulators will not turn our simulation off. 

Richard Carrier has written an entire rebuttal of the argument on his blog. He always answers comments under his posts, so if you disagree with some part of the rebuttal, you can just leave a comment there explaining which claim makes no sense to you. Then, he will usually defend the claim in question or provide the necessary clarification.

I would put more emphasis on this part:

Even the smartest people I know have a commendable tendency not to take certain ideas seriously.

Indeed, I think this tendency commendable and I do not take these ideas seriously. Like Puddleglum, I ignore and am untroubled by the whispers of evil spirits, even though I may not (yet) have any argument against them. I do not need one. Nor do I need to have an argument for ignoring them. Nor an argument for not looking for arguments. Gold Hat's line comes to mind:

“Arguments? We ain’t got no arguments! We don’t need no arguments! I don’t have to show you any stinking arguments!”

I can show you a vibe instead, if that helps, but it probably doesn't. Somehow, the Simulation Argument seems to me to not be doing enough work to get where it goes.

[ Note: I strongly agree with some parts of jbash's answer, and strongly disagree with other parts. ]

As I understand it, Bostrom's original argument, the one that got traction for being an actually-clever and thought-provoking discursive fork, goes as follows:

1. Future humans in specific, will at least one of: [ die off early, run lots of high-fidelity simulations of our universe's history ["ancestor-simulations"], decide not to run such simulations ].

2. If future humans run lots of high-fidelity ancestor-simulations, then most people who subjectively experience themselves as humans living early in a veridical human history, will in fact be living in non-base-reality simulations of such realities, run by posthumans.

3. If one grants that our ancestors are likely to a] survive, and b] not elect to run vast numbers of ancestor-simulations [ both of which assumptions felt fairly reasonable back in the '00s, before AI doom and the breakdown of societal coordination became such nearly felt prospects ], then we are forced to conclude that we are more likely than not living in one such ancestor-simulation, run by future humans.

It's a valid and neat argument which breaks reality down into a few mutually-exclusive possibilities - all of which feel narratively strange - and forces you to pick your poison.

Since then, Bostrom and others have overextended, confused, and twisted this argument, in unwise attempts to turn it into some kind of all-encompassing anthropic theory. [ I Tweeted about this over the summer. ]

The valid, original version of the Simulation Hypothesis argument relies on the [plausible-seeming!] assumption that posthumans, in particular, will share our human interest in our species' history, in particular, and our penchant for mad science. As soon as your domain of discourse extends outside the class boundaries of "future humans", the Simulation Argument no longer says anything in particular about your anthropic situation. We have no corresponding idea what alien simulators would want, or why they would be interested in us.

Also, despite what Aynonymousprsn123 [and Bostrom!] have implied, the Simulation Hypothesis argument was never actually rooted in any assumptions about local physics. Changing our assumptions about such factors as [e.g.] the spatial infinity of our local universe, quantum decoherence, or a physical Landauer limit, doesn't have any implications for it. [ Unless you want to argue for a physical Landauer limit so restrictive it'd be infeasible for posthumans to run any ancestor-simulations at all. ]

So, while the Simulation Hypothesis argument can imply you're being simulated by posthumans, if and only if you strongly believe posthumans will both of [ a] not die, b] not elect against running lots of ancestor-simulations ], it can't prove you're being simulated in general. It's just not that powerful.

My own take on the simulation argument is that it's true, but has no implications, because you can narrow nothing down other than pure logic, so it would be a problem.

(Here, I'm focused on the most general version of the arguments I've seen).

I don't see the phrase "self-indication assumption" in here anywhere.

Nothing is obviously wrong with it. I'm not sure what probability to assign it. Its sort of "out of sample". But it seems very plausible to me we are in a simulation. It is really hard to justify probabilities or even settle on them. But when I look inside myself the numbers that come to mind are 25-30%.

No one has refuted it, ever, in my books

Nor can you refute that my qualia experience of green is what you call red, but because every time I see (and subsequently refer to) my red is the same time you see your red, there is no incongruity to suggest any different. However I think entertaining such a theory would be a waste of time.

I see the simulation hypothesis as suffering from the same flaws as the Young Earth Theory: both are incompatible with Occums Razor, or to put it another way, adds unnecessary complexity to a theory of metaphysics without offering additional accuracy or better predicting power. The Young Earth Hypothesis says that fossils and geological phenomena only appear to be older than 6,000 years, but they were intentionally created that way (by the great Simulator in the sky?). This means it also fails to meet the important criteria of modern science: it can't be falsified.

To be able to falsify something means that a theory is valuable, because if it fails, then you've identified a gap between your map of something and the territory that you can correct. A theory becomes even more valuable if it predicts some counter-intuition or result which hereto none of our models or theories predict, yet repeated tests do not falsify it.

Simulation Hypothesis intrinsically means you cannot identify the gap between your map and the territory, since the territory is just another representation. Nor does it explicitly and specifically identify things which we would expect to be true but aren't: again, because everything would continue to appear as it always has been. So it offers not value there.

Simulation Hypothesis isn't taken seriously not because it can't be true - so when you see green I see red - but that you can predict no difference in my or your behavior from knowing this. So what?
 

For an argument against the sim hypothesis see https://lorenzopieri.com/sim_hypothesis/  or the full article https://philpapers.org/rec/PIETSA-6  (The Simplicity Assumption and Some Implications of the Simulation Argument for our Civilization). 

In a nutshell:

0- Suppose by absurd that we are in a simulation. 
1- We are equally likely to be in one of the many simulations.
2- The vast majority of simulations are simple [see paper to understand why this is reasonable].
3- Therefore, we are very likely to be in a simple simulation.
4- Therefore, we should not expect to observe much complexity.
5- But we do observe complexity, therefore we are very unlikely to be a simulation. 

Humanity gets to choose whether or not we're in a simulation. If we collectively decide to be the kind of species that ever creates or allows the creation of ancestor simulations, we will presumably turn out to be simulations ourselves. If we want to not be simulations, the course is clear. (This is likely a very near-term decision. Population simulations are already happening, and our civilization hasn't really sorted out how to relate to simulated people.)

Alternatively, maybe reality is just large enough that the simulation/non-simulation distinction isn't really meaningful. Yudkowsky's "realityfluid" concept is an interesting take on simulation-identities. He goes into it in some depth both in the Ultimate Mega-Crossover and in Planecrash.

Bostrom's argument may be underappreciated. You might like Roman Yampolskiy's work if you're deeply interested in exploring the Simulation argument.