This question seems to be distinct from some of the others in that it requires insight to answer, not just insight to ask.
"Noticing" is at the interface between conscious and non-conscious processes. You can't deliberately bring something to your attention, unless it was already in your attention. Most of the rationality advice here is about how to do the right thing with what has come to your attention. But how does one learn to notice the right things? One way is deliberately directing your attention where there is likely to be something to notice -- hence all these "useful questions". Another is practicing habits of thought, by routinely asking these questions.
See also: Boring Advice Repository, Solved Problems Repository, Grad Student Advice Repository, Useful Concepts Repository, Bad Concepts Repository
I just got back from the July CFAR workshop, where I was a guest instructor. One useful piece of rationality I started paying more attention to as a result of the workshop is the idea of useful questions to ask in various situations, particularly because I had been introduced to a new one:
"What skill am I actually training?"
This is a question that can be asked whenever you're practicing something, but more generally it can also be asked whenever you're doing something you do frequently, and it can help you notice when you're practicing a skill you weren't intending to train. Some examples of when to use this question:
Many of the lessons of the sequences can also be packaged as useful questions, like "what do I believe and why do I believe it?" and "what would I expect to see if this were true?"
I'd like to invite people to post other examples of useful questions in the comments, hopefully together with an explanation of why they're useful and some examples of when to use them. As usual, one useful question per comment for voting purposes.