You could start by trying to force close the Music app, followed by resetting your phone: double-tap the home button, locate Music at the bottom (swiping if necessary), tap and hold it until it wiggles, tap the minus sign. Now reset your phone: hold the on/off and home buttons until you see the Apple logo (ignore the off slider that appears first), then release. If that doesn't fix it, then confirm that this problem exists with all playlists. If it doesn't, you may have to delete the playlist in itunes, sync your phone, then recreate it and sync again as something may be corrupt with it. Otherwise you'll have to proceed with restoring your phone (http://support.apple.com/kb/HT1414), first by making a backup at step 6 and restoring to this backup at the end. Then sync to transfer your music back and try your phone again. If that fails you will have to save as much of your data as possible then repeat the restore process but as a new iPhone rather than from backup. Before restoring your phone be sure to import your photos to your computer and back up your contacts (to iCloud, Google, Outlook, or something). Missing photos and contacts are the most commonly reported issues after restoring.
