Neither of your definitions of critical thinking fits the way I've seen the term used. The sense of "critical" in the widely-used meaning is closer to your 2nd definition ("a critical2 response means a response ... that focuses on flaws") though this use of "critical" is not strictly negative. A book critique might be a rave review, e.g., and can be so even when the critic employs critical thinking.
Secondly, I am inclined to disagree with your conclusion that "people end up only challenging the things they disagree with" when they think critically or that "critical2 thinking skills help people resist changing their minds". This may be true often enough, but critical thinking, when done right, is critical[1] of all relevant ideas.
Caveat: no dictionaries or other references were consulted in the writing of this comment; this is just a brain-dump.
[1] Here I use critical in the sense of examining closely with a willingness to pass judgement.
Agreed. I have always taken "critical thinking" to mean thinking carefully, not just believing everything you hear, trying to avoid bias, etc., etc., etc., and so far as I can tell other people's use of the phrase generally has a similar meaning.
The way I would use the word, critical thinking is a subset of skepticism: it is skepticism directed at ideas that you have already accepted, or are in danger of accepting; especially skepticism directed at your assumptions. Searching for flaws in ideas you already don't like isn't critical thinking.
This probably isn't emphasized too much in a school setting whenever you're encouraged to think critically, because the usual tendency is to believe everything the teacher tells you.
I sometimes hear teachers use it to describe reasoning involving any sort of deliberate thought at all, as opposed to the chomskybot-like "B.S." (is that a colloquialism in the context of school assignments?) that many students turn in.
For quite a while, I've felt that my mind contains important insights which are getting held up because I don't write enough. So to encourage myself to write more, I've started a blog: Concept Space Cartography. My most recent post there, Two Definitions for Critical Thinking, is likely to be of interest to Less Wrong.
Also, every page on my blog has an embedded copy of Textcelerator, a tool I created for speed-reading. (It's normally a browser plugin, which makes it appear on every web page. But you can use it on my blog without the plugin.)