Yikes, that's a new one to me.
If you routinely see behavior that weird after only a few days turned on there's something wrong with your OS install (or, possibly, hardware, though that seems a lot less likely). Once in a while minor glitches can crop up when a Mac hasn't been restarted in a while, but I routinely leave computers on for weeks or even months at a stretch without issue.
Have you installed any system hacks or anything else system-level like an antivirus scanner?
If not, I would have to suggest you get out the discs that came with the computer (or OS upgrade discs, if you have them) and do an Archive and Install, preserving users etc. Then of course keep doing Software Update until everything is current. That should be relatively painless, if somewhat time consuming, and if the problem is with a bum OS install it will fix it.
If it doesn't help, you could try creating a new user account and using that for a while to see if it also displays the issues--if not, then it's bad prefs in your user account and you can start from there. If so... well, not really sure.
Do also make sure you have a current backup, regardless, but that's good advice whether anything is acting up or not.