Problem with data on external hard drive

If, when the drive was almost but not completely full, you copied the movies that are skipping over there's a chance they are badly fragmented, which could cause reads to be so slow that they skip. Never seen fragmentation THAT bad on a modern computer, but it's possible.

However, that wouldn't explain why they would stall in the middle--that's normally a sign of a corrupt video file (99%) of the time, or hardware problems (the other 1%).

First thing to try: Open Disk Utility (it's in the Utilities folder in your Applications folder), select the drive in the list on the left side of its window, and click the "Repair Disk" button over on the lower right. See if it shows you any errors; if so, do it again and see if it managed to fix them. This will tell you if there's some obvious directory (software, that is) problem with the drive. If it finds something there's a chance the problem happened due to the drive being overfull, though in theory that shouldn't cause corruption of any sort.

If it finds and fixes something, see if they play now. If so, make sure you have a backup of anything important on the drive (which you should under ANY circumstance anyway), and just keep using it with an eye out for problems.

If it finds nothing wrong or the files are still skipping/stalling, try copying one to the internal hard drive and see if it still misbehaves. If it works on the internal drive then it's either fragmentation or there are intermittent read errors on the drive. If it also skips/stalls on the internal, then either the files were corrupt to begin with (did you test them before copying them? I've seen a LOT of bad video files offered for download) or something happened to them when you copied them to the drive or afterward. Which is hard to say without continuing to use/test the drive.

Two asides: To play bad files, under any circumstance, some video players may have luck where others do not. I've seen files that VLC or QuickTime player can't deal with, but Mplayer OSX Extended can, and I've seen messed up AVIs that Mplayer stalls immediately on while VLC plays ok after hiccuping on the bad bit.

And, I've read about a LOT of problems with LaCie externals due to bad power bricks (or possibly other quality control problems). example thread at MacInTouch. In fact, some of the reports of erratic behavior due to flaky power sound rather similar to what you're describing.

And of course it's ALWAYS possible for hard drives or other hardware to die entirely on their own, regardless of how much you baby them--there are moving parts that will eventually fail no matter what, and nothing physical is immortal.

So don't rule out hardware problems.