Consequentialism traditionally doesn't distinguish between acts of commission or acts of omission. Not flipping the lever to the left is equivalent with flipping it to the right.
But there seems one clear case where the distinction is important. Consider a moral learning agent. It must act in accordance with human morality and desires, which it is currently unclear about.
For example, it may consider whether to forcibly wirehead everyone. If it does so, they everyone will agree, for the rest of their existence, that the wireheading was the right thing to do. Therefore across the whole future span of human preferences, humans agree that wireheading was correct, apart from a very brief period of objection in the immediate future. Given that human preferences are known to be inconsistent, this seems to imply that forcible wireheading is the right thing to do (if you happen to personally approve of forcible wireheading, replace that example with some other forcible rewriting of human preferences).
What went wrong there? Well, this doesn't respect "conversation of moral evidence": the AI got the moral values it wanted, but only though the actions it took. This is very close to the omission/commission distinction. We'd want the AI to not take actions (commission) that determines the (expectation of the) moral evidence it gets. Instead, we'd want the moral evidence to accrue "naturally", without interference and manipulation from the AI (omission).