I had exactly the same issue on my 5th gen iPod Touch, the only thing that sorted it out for me was downgrading to iOS 6.1.3. Everything is syncing as it should now, even when using iTunes 11.1 to do it.
All in all I ended up wasting two days trying to fix it. It all started for me when I upgraded to 7.0, suddenly I noticed that I could no longer sync new music to my touch, I would have the spinning circle icon and the songs would be greyed out on the iPod itself. I tried on two different PCs, both with iTunes 11.1 installed but neither would sync.
So I decided to do a clean install of iOS 7 hoping that would fix the issue. I spent almost 2 hours syncing my music and to make things worse, had iTunes messages every now again saying "This track could not be synced. The file format is not valid" - even though the tracks were either MP3 files or iTunes purchased music. Simply dragging them onto the iPod again worked which I found really bizarre. (Potential iTunes 11.1 issue?) Then I went to play a song and found that none of the tracks were playing, the sync had completely failed. I watched my iPod skip past every single song.
So again, another restore on another PC. this time I went into DFU mode to do it but exactly the same problem, now with the first issue re-occuring once again of not being able to sync.
Ended up thinking iOS 7 was not worth the hassle and downgraded to 6.1.3 and guess what, no issues. Everything has synced perfectly, no skipping tracks on the iPod.