I just found this very interesting link on the Apple discussion forums regarding my MacBook and its video card. An excerpt:

“…someone mentioned that Apple knows internally that it is an issue with the solder connection between BGA packages and the main board. These machines came out right around when manufacturers were just starting to become ROHS compliant, (the standard that forbids the use of solder containing lead in electronics,) and so it is not surprising to me, (having dealt with some similar issues from the point of view of the manufacturer at work,) that these problems are happening. The lead-free solder is much more brittle than the old kind and solder joints that crack after many thermal cycles are a common problem that everyone trying to use the lead-free solder has had to confront.”

There’s some suggestions about deleting some of the video drivers that basically disable the video card; I’m going to run and get my machine to see if the quick fix works.