In my experience, the songs that are skipping may not have transferred over to your iPod correctly. I would advise you to uncheck the "Sync Music" checkbox, and apply the changes (so there is ultimately no music syncing to your iPhone).
Once you have done that, recheck the "Sync Music" checkbox, and apply the changes once more. This will instruct iTunes to completely remove all music from your iPod, and then copy the files once more. If you have a large amount of music, this initial sync may take a while.
If the above does not resolve your issue, see the following articles: