(registered to ask about this then saw it was a known issue)
Now, I'm a complete Java and OpenGL newb (or perhaps even less given as I've never done anything with OpenGL) but from a few Google searches it looks like this particular error (1281) is an error relating to the maximum texture size that the graphics card can handle. Perhaps Notch's updated renderer is stitching together textures that are slightly too big for some machines to handle?
I know I'm on a MacBook with an integrated chipset (hooray D: ) but this is just my barely-educated guess at what the problem might be, despite the fact Notch already likely both knows what the problem is and is probably halfway to fixing it by the time I've made this post.
EDIT: Oh, and for reference, Firefox 3 on Mac OS X 10.6 with Intel GMA X3100 chipset.