It was pretty simple to write some code for our Community site which fires early enough to log problems that occur during page load (and later). What I did end up doing, which was a bit more fancy, was queueing the errors until more of the site has loaded.. by then we have access to some analytics libraries (Omniture) which we're going to use to record the errors & report on them (as well as being able to set alerts).
This is the kind of thing that gets recorded;
The implementation is pretty lightweight, since it only relies on things that we've already got in place.
Does anyone else use this kind of thing on their site?