First, the fact that you want to solve this problem... is probably a problem in and of itself!
But regardless, what you want to do requires two operators which do not presently exist: $unravel and $typeof.
The hypothetical $unravel operator can split up a document into key/value pairs. The even more hypothetical $typeof operator can allow you to match for values of the date type (note that you can emulate $typeof currently, but I'm not going to explain how as it's quite complicated and not useful without $unravel).
You can
vote for $unravel here. In the meantime, you can achieve what you want through map/reduce, by writing appropriate Javascript to iterate over document values and emit the fields that have a type of date.
Regards,
John