Can QuickTime Pro Edit mp4 files?
I think the short answer (one you may have already found) is no! I'm in a similar situation: I write music to picture and used to receive clips as .movs. I could then add final audio myself for showreel/web purposes. Now those clips arrive as mp4 and are useless and unchangeable. I can merge files in QT pro for viewing, but no saves are allowed.

Editing software usually prefers 'linear' formats (aiff or wav for audio, .mov or similar for vids) whereas mp4 is heavily compressed and 'lossy'. Also, the key frame rate is very poor (300 I think) so that might explain some of your edit problems. The only workaround I can find is to open in QT and re-export, but the results are pretty ugly! Saving to mp4 for final product? Why not - it looks pretty and the file sizes are good. Working with mp4 in the edit? Hell no :)