To view MPEG2 in Quicktime, you need the QuickTime MPEG2 component. This is an extra cost (it does not come with QuickTime Pro) and you can get it from apple.com.
But, even then, you still cannot edit MPEG2 with Quicktime. It will let you export to another format (if you have QuickTime Pro), but this is impossibly slow (well, it is on my G4) and (in my experience) prone to crash.
There are some other apps out there that can help. AFAIK they all rely on the MPEG2 component of Quicktime. MPEG2 Works is shareware and looks comprehensive, but I haven't got a clue how to use it. However, I did manage to do some basic trimming of an MPEG2 file using MPEG Streamclip. It seems to have additional features too, but I've not investigated them yet. Best of all, it's free (although you still need to buy the QT MPEG2 component).
The akwardness is because MPEG2 is not a format that is intended to be editable. It's main use is for distribution (eg, DVD, Digital TV).
HTH.
SL