After Jesus rescues Santa from the Iraqis he hands Santa a black silenced pistol. After Santa kills the torturer and turns to run away he is holding a silver revolver.
At 4:10 there are two boxes of items to Cartman's left, but moments later at 4:20 the number of boxes and their contents changes.
At 12:59, The Iraqi soldier interrogating Santa says "Your country is sick." However, the North Pole [where Santa is from] is not part of any one country/nation.
Talking and singing are processed in different areas of the brain; thus, Jimmy's stutter should not affect his musical performance.
At about 15:04, the second time in this shot where Santa is being electrocuted, his hands disappear.