Songs Will Not Play
A common issue that comes up with iPods, and not just iPod Shuffles, is that a particular song will not play on your device that you are trying to sync over. There is actually a way to troubleshoot this for your iPod in a step-by-step way since there are a number of concrete reasons that this may be occurring on your particular device.
First, you should go look at the files in iTunes. Make sure that they are still consistently there as individual files on your computer and not absent spaces that are just being indicated in your iTunes library. You will usually be told about this during the sync, unless you had previously turned off the warning. In this situation you should either re-upload them to your computer and then re-link the files, or simply remove them from your iTunes library.
You should also make sure that both your iTunes and your iPod Shuffle's software are completely up to date, which is the cause of a great number of issues that need iPod Shuffle help. You can do this by searching for updates in iTunes, and once things are completely up to date you will have saved yourself a number of different problems.
If you find that there are certain songs that you bought from iTunes that are not playing on your iPod Shuffle then you can apply a separate troubleshooting process to that. Make sure that your computer is properly authorized with iTunes, and you may even want to un-authorize and reauthorize the computer.