The Server Error log is quite useful in tracking down problems. There are currently only two options - maintain the log and keep looking at the "Server errors have been logged. You should review these." message in the AdminCP or delete the log to get rid of the message. I'd prefer a 3rd option - dismiss the notification but maintain the log, and have the message then reappear with subsequent errors. So we'll know there's a new error or errors. In this case, some better control over pruning older entries and keeping newer ones might be nice as well (e.g. delete log entries prior to X date).
In theory though, shouldn't you not wait to fix the errors in the log?
[2 cents] I think a possible "export error log" may serve a valuable function however if you want to save & keep track of old archived errors for future reference. I don't see a valid purpose for dismissing the notification. If I did that I would simply forget which I fixed & which are still outstanding.[/ 2cents]