Crucifixion stigmata occur after being nailed up, so the holes in the feet wouldn't be present during the whipping; also, nails through the palm, sometimes even the wrist, won't support a body without having the limbs roped to a support, and/or having the feet propped on a support, all of which are only occasionally portrayed.
Around 5 minutes in, when Dean is texting Mary, it is fairly obvious that Dean isn't actually the one typing. For example, the question mark appears without him switching to symbols, and even after the message has finished, he continues to type.
The autopsy report says the corpse's skull was filled with a gooey substance. The corpse is shown with the skull intact and all the hair in place. In order to make the determination noted, the skull would have had to be opened which would necessitate cutting the scalp.