A flashback scene shows that Morgan was involved in Garcia's recruitment. But an earlier flashback scene showed their first interaction as occurring when Garcia was already hired.
The black SUVs used by the team frequently have US Government "G" plates. However, the plates are usually incorrect for the type of vehicle they are on. Plates with prefixes of G12 and G14 have been seen. G12 is a compact sedan and G14 indicates a large sedan, and would be incorrect for use on an SUV. The correct plate prefixes would either be G41 for a 2 wheel drive or G61 for a 4 wheel drive 1/2 ton vehicle.
Agent Rossi reveals the anniversary of the traumatic death of the parents of the three siblings to be 20 years, but in an earlier episode he says that it was the 21st anniversary.
Even though the BAU's office is located in Quantico, VA, most of the team members live in or around Washington, DC. This is very unusual. DC is a high cost of living area, but Quantico is less so. Quantico is also 35 miles south of DC. It'd make more sense for the team, who often need to respond quickly, to live in the Quantico area.
The series has many instances where records that would only be stored in print form are actually stored digitally. These include employment records from closed businesses, foreign birth/death records and incorporation documents where the participants are seeking anonymity.
While the show has used different model GulfStreams,they always have the same interior. There have been minor changes in the interior over the seasons. The size of the cabin shown is most likely the G450 or G550 which have similar interiors. A G100 or G200 is a much smaller cabin, narrower and not as much headroom when walking in aisle.
Most serial killers are either caught in the act, caught due to extreme carelessness on their part or confess when they are arrested. Almost none have ever been caught due to the result of profiling by the FBI or any other agency.
Violations of the Fourth Amendment are so numerous in this series that they have become a joke. The profilers on the show routinely break into homes and businesses, hack into laptops and cell phones and seize evidence from crime scenes while never obtaining the necessary legal documentation to do so.
On several occasions, cases have taken place in Southern Virginia, Maryland and Pennsylvania all within several hours driving time from the BAU's QUantico headquarters. Yet the group is shown flying there in the executive jet available to them, a process that would actually take longer than driving, if flight prep time and travel to and from the plane are included. It would also be far more expensive.
It's very unlikely that a government agency would pay for extravagant travel when cheaper options are available.