I have the same exact problem, and maybe the solution?
I have a brand new 120 GB, 6G iPod Classic, (fully updated) less than a month old I put all my music on it (I have about 22 gigs worth) and I started using it. I mostly play music via playlist and shuffle. In the MIDDLE (or end, the point is, the song would be playing fine) of a playing a song in a playlist it would decided to skip to the next song (no pattern to when or which song it would skip, it was just random) The first time it happened, I was like okay, weird, skipped back, and it played the same song all the way through with no problems. Then a few songs later it would do the same thing. Again, completely random.
I started researching like crazy over the past week, and discovered it was a pretty common problem. I read a number of possible explanations, it was a hardware defect, it was a software defect, there was a problem with the new iTunes transferring songs. I decided to pursue the latter. I read into it some, a lot of people seemed to be convinced there is a problem with the new iTunes and transferring a large quantity of music. I read someone recommend a program called Mp3 Validator that scans music files and fixes and problems that may cause them to skip. (presumably why the songs worked fine in iTunes but skip randomly once transferred to the iPod)
Anyway, to make a long story longer, I tried the program, scanned the music files directly off my iPod music directory--it fixed a couple hundred problem files. I had it going today, just playing through the playlist, got through 10-12 songs without any skipping. Granted, it wasn't an extended listening session, but I'm holding on to hope.
I can't say for sure that this fixed the problem, or if it even WAS the problem (for all I know it COULD be a hardware defect). But if you are getting REALLY frustrated by the random skipping, you could give it a try.
I'll definitely be having an extended play session with it this weekend, so I can give you an update on whether it is a surefire solution or not.