Towards the end, Reid takes off his Kevlar vest. The next scene with him shows him walking towards the front door of a house, and the vest is back on. When he opens the door, the camera angle changes and shows him walking in through the door, and the Kevlar vest is now gone again (and remains missing).
Prentiss stated that the upside down cross looks like satanism. This is a common mistake. Although Satanists do use the inverted cross as a symbol, and true satanists would never kill, devil worshipers would kill though. The upside cross is a Christian symbol know as the cross of St Peter or St Peters cross. Peter felt that he was not worthy to die the same way as his savor Jesus so he wanted to be crucified upside down.
When Hotch and Prentiss are in the victim's room in the beginning, Hotch says the unsub turned his crucifix upside down. This is incorrect; a crucifix is a cross with an image of Jesus on it. What was on the wall was just a cross made of many shells. This mistake is becoming more and more common particularly from people with protestant backgrounds, but any catholic would know the difference.