That is VERY strange! Sounds like there are errors or something has corrupted.
I have imported DWG files from other programs and have seen corrupted object or models.
I would try downloading Sketchup 8 again and re-installing it.
Also, maybe update Windows too.
I have never seen that problem before. As if the snaps were not working correctly. When it pops up with "Endpoint" it always means the very end of the line.
Check your snap options too under Window/Model Info/Units
Maybe the "Enable Length Snapping" is set at a strange unit...
I mostly work in feet so I use .01'
Let us know what you figure out