The only way to delete photos on your iPad that were put there during a sync is to do another sync. But this time in itunes uncheck the albums you do not want on your iPad then click Apply.
I suggest you do this but uncheck all photos then tap Apply so that all photos that were transferred from your computer to your iPad are deleted from your iPad. Then delete all other photos on your iPad that might have been obtained from email, web sites or taken with the iPads camera.
After you do this quit the photo app.
Go to the Home screen and double click the Home button. That will reveal the row of recently used apps at the bottom of the screen. Tap and hold on the Photos app until it wiggles and displays a minus sign. Tap the minus sign to actually quit the app. Then tap anywhere on the screen above that bottom row to return the screen to normal.
Then reboot your iPad. Press and hold the Home and Sleep buttons simultaneously ignoring the red slider until the Apple logo appears. Let go of the buttons and let the iPad restart.
Once your iPad restarts you could add some photos from your computer by syncing. Hopefully the problem will be fixed.