Any help with this issue would be greatly appreciated. I'm on OS X with the latest version of Quicktime Pro.

I've downloaded a number of MPG videos through Limewire, usually 10-20 MB in size, that open fine in Quicktime.

The weird thing is that the indicator icon that moves along the bottom of the Quicktime screen makes it all the way to the end, as though the entire MPG has been shown, but the clips end about 30 seconds into each one.

And here is where it gets really weird. At the very end of the 30 seconds, the image on the screen skips ahead to another part of the clip entirely. So, when you slide the indicator back (to rewind) you're in an entirely different part of the clip.

It's as though the clips are "layered" into 30 second increments.

Anyone have any idea what this problem is or how to fix it?

Ron, apparently you never went back to the Apple Discussion forums to look for your answer. A nice lady explained what was happening and how to fix it. A program called Rosetta fixes clips that were improperly assembled, and there are also free programs available to repair mpgs that were created on Windows that will not play on the Mac OS.
Anybody else having this problem would do well to use the Apple Discussion forum for QuickTime for Mac OS. For years I wondered what was going on, but then again, I didn't ask.
But if you do ask, please follow through on your postings and give results. It not only helps you, which I realize is your first intent, but it can also help others who struggle through the same issues.