Letter for Advisor's Promotion I've been asked by my former department to write a letter for my doctoral advisor's promotion. What kind of information do departments typically want in these letters? 

They specifically asked to mention any areas for improvement. While I got along with him very well overall, I can, with hindsight, see some areas in which he could improve. To what extent would this hurt his chances for promotion?

Thanks!
Write about what you know and don't speculate. Because of the power imbalance, let others (professors) speak about improvements. 

Think about whether you have had a good experience and whether you would recommend him to other students. Make it personal. If some sorts of students might not thrive with this prof and you wouldn't recommend they work with him you can say that. 

Be honest, but don't stray too far outside the limits of your relationship. 

From a student I think that is all that is expected. 

If you think he needs improvement, speak to him about it, privately. And preferably after you finish. "I wish that ..."