The auction clock shows a 29 minute difference in time from when Katie Cole is sitting at her desk in Maryland to when the team watches the live feed in their conference room in Virginia moments before Cole arrives. General flight time from Maryland to Virginia is around 30-40 minutes. Even with more efficient transportation such as a private jet (something less likely for Cole to have access to as she no longer works for the FBI) it is very unlikely that Cole gets from her desk to the conference room in half an hour.
Although the headmaster identifies himself to 'Hugz' as Hayden (and is credited as such), he is referred to as Howard when the unsub hears the broadcast about his arrest.
The unsub's car has a Virginia license plate 721-LFDZ. Current Virginia plates have the format of 3 letters and 4 digits, not 3 digits and 4 letters.
Early on, a chatter gives his website address as an IP address with a 4 digit quad. IP address quads can only fall within the range of 0 to 254 inclusive. This is likely so that someone's actual IP address isn't compromised.
When the BAU jet is shown in an overhead shot as it heads to Cleveland at the beginning, the jet's registration numbers are reversed as if in a mirror, revealing that the shot is "flopped" to reverse the image.
They are supposedly in Virginia, and the cars have Virginia plates, but when the bad guy changes his car radio to 106.7, the radio displays the call letters of Los Angeles radio station KROQ.
When JJ and Garcia try to read the 4-digit number, the first digit is clearly a 3, and the last one is a 6, although not so clear. For some reason Garcia ignores the leading 3, so instead of 99 number (3006 through 3996), she says that she has to search through 999 numbers ending in 6.
JJ tells her media contact the FBI is looking for a 4-foot tall boy with brown hair and the news report says the FBI is looking for a boy 3 feet tall with sandy brown hair.