That definitely sounds frustrating. If the songs are not playing fully in iTunes, they may have not downloaded completely. See the following article:
Occasionally, if a song purchased from the iTunes Store on a Mac or PC was not downloaded completely, the song may not play back fully. The song may abruptly stop during playback, and iTunes may start playing the next song in your library or playlist.
If iTunes in the Cloud is available in your country, try the following steps to resolve the issue:
1. Delete the purchased song that is exhibiting the problem from your iTunes library.
2. Click on the Purchased link in the iTunes Store to view your previously purchased music.
3. Download your previously purchased song from this list.
Note: iTunes in the Cloud, which allows you to download previously purchased songs from the iTunes Store, is not available in every country. Learn if iTunes in the Cloud is offered in your country.
Once you have re-downloaded the content, and verified the issue is resolved, simply re-sync the music to your iPod and Enjoy!