In this episode right before Spencer goes to JJ, he checkmates Gideon. But in later episodes with Prentiss it's stated that Spencer has never beaten Gideon.
When Gideon gives Reid the Redskins tickets, each time the camera angle is on Reid he's holding the tickets facing toward him, but when the camera angle is on Gideon, he's holding them facing away from him.
When the team members are listening to the un-sub ranting on the phone, the Rubik's cube in front of Reid changes position from one shot to the next (orange and green sides showing, to yellow, then back to orange and green). This occurs about 26 minutes into the episode.
This episode is set in San Diego, which conveniently looks very much like Los Angeles, where the series was filmed. But shortly before Gideon figures out the identity of the unsub, as he and Elle sit in their car, a street sign is shown for the 15700 block of Hesby St. There is no Hesby Street in San Diego, but there is one in North Hollywood in Los Angeles.
Gideon and Morgan go to one of the crime scenes. Neither one is wearing gloves, and Morgan goes so far as to touch and disturb elements of the scene. Seasoned members of law enforcement would never do these things.
For their stakeout, the team is seen sitting in higher-end vehicles as a means of camouflage - a way to blend in in upper class neighborhoods. However, Reid and Morgan are seated in a bright red vehicle, which would not be preferred in a stakeout because the bold color would tend to have the opposite effect.
The poem that the unsub wrote on the mirror ends with "on the owner's light." In this context it should read "on the owners light."