David Rossi's moustache and beard gets longer and shorter between scenes. It's long when he's preparing for his interview with Erin Strauss, clipped during the interview itself, but back to long for the next scene.
When Agent Morgan comes out from behind the trees after reenacting the unsub's strategy, he has a leaf on his head. The camera switches to the house for a second, and when it switches back, the leaf is gone.
When Agent Prentiss finds a cellphone, the Carrollton detective quickly looks at the phone, and declares that '972' is the Carrollton area code; in actuality, 972 is the main prefix for most of the Dallas-Fort Worth area, and the counties stretching north and east of the two cities.
When Hotch asks Morgan to search the 7th floor, he is seen in the next scene talking to a woman in front of room 104. If he were on the 7th floor, the room number would be in the 700s.
When Hotch introduces Rossi to the team, he refers to Emily as "supervisory special agent" but when they are in the room with the round table, you can see Emily's badge and it says SA instead of SSA. Meaning that according to her badge, Emily is only a special agent, not a supervisory special agent.
When the FBI agents draw their weapons and kills the villain, there are at least five policemen at their sides and behind them. All of them have their weapons up, except the policeman closest to the shooting. He is more in danger then anyone else, but stands there like a buffoon.
The team acts surprised when they find out one victim was able to purchase a shotgun and leave with it the same day. Since this is the normal legal procedure in the vast majority of U.S. states, this should have been no surprise to a federal agent.