If you have not restarted the iPad recently, you should probably do that first.
Photos synced through iTunes can not be deleted on the iPad. Check the folders you chose to sync in iTunes and see if you have duplicates there. Also Check your iTunes Photos sync settings (iPad must be plugged in to see these).
If the synced albums are still duplicated, you can try turning Photo syncing off in iTunes and then syncing to remove them. Check to see that they all went a way. Then turn them back on to sync again. If you have a lot of photos, this could take a while.
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When you have problems with an app it's a good idea to close it.
Close: With the problem app closed, double tap on the Home button to get the multitask bar. Tap and hold on any icon in the bar until they jiggle, then tap the minus sign on the problem app. This will remove it from RAM and insure a clean start the next time you launch the app.
If that does not work try a restart,
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears.