It would be useful if the API allowed you to return items based on their last activity date. Let's take a question for example. 

/questions/fromlastactivitydate=XYZ&tolastactivitydate=XYZ

All questions having been created, edited, commented on or answered on as their last activity during the requested period would be returned.

There is already a last-activity field returned in the API, so I assume it would be a trivial concept to implement. It would be great if that could also be applied to Users as well.

The returned values should only include the activities that took place during that period of time, for example, only comments and answers that have been made during the requested period.

A possibly more complex, but related, query would be to provide an activity period, which doesn't have to be the last activity date of a question, and the returned values would be all questions which had activity during said period and including only answers/comments that were made during that period.