Does anyone know of software that can be configured to automatically login to a website, perform tasks, and take screenshots at regular intervals? Preferably Mac-compatible.
Sounds like FakeApp is what you're looking for.
iMacros can probably do what you need. We use it in a commercial environment and it is very effective.
Since "performing tasks" can mean so many different things, there most likely isn't a program out there, that would fully satisfy your needs. There are programs automatically logging you in (LastPass is a good example), there are programs taking screenshots, but if you want a all-in-one solution you probably need to let somebody write that software for you (or do it yourself).
If you're willing to script it,watir might do everything you need. Not sure if it does real screen shots or just captures of the HTML though.
I use AutoHotkey to do this. This is an example of a script that logs into a website.