Can I put a widget inside a folder?
After much experimenting, it is apparent that you cannot put a widget inside a folder. Folders will only hold shortcuts.

I have a stock Motorola Droid with Android 2.2.1. Admittedly, there may be a ROM out there that lets this happen, and perhaps even a customized version from some carrier/manufacturer that allows it. But without significant modification, this just can't be done.