I can get in-progress and completed dates for user stories and defects but not for tasks except by looking at revisions for each individual task which is very cumbersome.
As you've discovered there's not really a "cycle time" concept for tasks in Agile Central, and there are no fields in the Task object that you could use for this measure. As I understand it tasks are intended to be work items with a pretty short lifecycle so actual hours on task are about the only measure of task duration that you're likely to find.
If your business need is critical then you could work with CA Technical Services and see whether you could get an app for this that leverages the Lookback API but I'm not sure how much value you're really likely to get from focusing on Tasks as opposed to the "first class citizen" items like stories, etc. Wish I had a better answer for you but I hope that helps.
Yes, I agree that tasks should have a short lifecycle. However, we are having problems with a couple of developers who are taking too long on an individual task but not marking the actual time very accurately. In a very few of the cases, the tasks should have been broken down more but mostly these developers are in need of some encouragement. And, I want an easier way as their manager to know when to step in.
Just to add on to the great information that Eric provided one possible workaround would be to use the Last Updated field. It isn't exactly what you are looking for, but may be useful in determining if further review is necessary. I know it isn't ideal, but I hope it helps in some way.
What method do you use now to "get in-progress and completed dates" for User Stories?
You can see that as columns on the iteration status page
Retrieving data ...