When the demon breaks through the door, he breaks most of it away and starts to walk through. In the next shot, he breaks it again, identically to the first time, and then just stands there.
The doctor is shot twice in the bulletproof vest yet it seems to have had absolutely zero effect on him. While the vests are proven to be very effective at stopping bullets, the cause a distribution of force across a wider area and still cause a significant impact to the body of the wearer. Significant bruising is common, and the wearer will be in significant pain, if not stunned momentarily. The doctor, however, is carrying on like nothing happened at all.