After hearing numerous reports about a problem with early "Rev A" MacBooks shutting down, I was comforted by the fact that I had not experienced this problem. Unfortunately for me, my MacBook exhibited its first signs of RSD (Random ShutDowns), also known as RSS (Random Shutdown Syndrome, not to be confused with Really Simple Syndication), yesterday morning.
If I'm not letting the MacBook do anything overnight, I usually put it to sleep when I head off to sleep. However, 3 minutes into having woken up the MacBook, it just turned off. It took several boots to get it to the desktop again, as it kept shutting down on its own. Fortunately, it seems like I can avoid this completely by not letting it sleep. I thought the case might have had something to do with load, but encoding an MPEG file to DivX proved that theory wrong.
So I trekked out to the Apple store yesterday, got an appointment at the Genius bar and then came back an hour later. Luckily, the Genius helping me out was "in the know" and knew about this problem right off the bat. He ordered a new heatsink and told me to come back when they call me. He wasn't sure why, but he said that whenever they replace the heatsink it fixes everything. Maybe this is a valid explanation. Everything seems like it will be taken care of from warranty, as I don't have AppleCare or ProCare.
As far as other MacBook problems are concerned, my early white MacBook exhibited signs of discoloration. I let the Apple Genius know about this and he also ordered the "top case housing with keyboard" which runs 101.56 but is covered under warranty (since Apple claimed this as a defect in the plastic a while back).