Hi Sara,
In my experience, the songs that are skipping may not have transferred over to your iPhone 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 iPhone, 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:
iPhone and iPod touch: Songs or other audio content are skipped during playback
http://support.apple.com/kb/TS3159
Troubleshooting songs that skip
http://support.apple.com/kb/TS3217
Cheers!,
Matt M.