My friend Brendan has put up a great post on his blog about questions to ask yourself on an alpine rock climb. I think my favorite thing about it is the mindset it conveys of always thinking, and always asking questions in the alpine environment. That's how you stay alive.
Here are a few more questions I'd add.
On the whole climb:
How is the altitude affecting my partner and I?
At the base of the climb:
Do I have my helmet on?
How do the route conditions look up close? Is there snow or ice that presents a hazard?
Do I know what my next rappel looks like? Do my ropes reach that point? What are my options if they don't?