Continuity mistake: The BAU has its 'own' airplane in use at the FBI. However the type of plane used varies between episodes and even within an episode (and even for at least one episode within one shot; see previous post). Although it would be likely for the BAU to have one dedicated airplane at least within one episode, it could be they time-share and so different planes are used. No matter what plane they are using, one thing never changes and that's the interior of the planes. So even when a different type of plane is used (e.g. Gulf Stream V vs. 100), the interior remains the same.
Continuity mistake: In episode 13 from season 5 "Risky Business", in the end scene a shot is shown of the FBI airplane in mid air. The airplane shown is a Gulf Stream V; which has a very distinctive nose. After the scene inside the airplane; another shot is shown of the plane's exterior, however all of a sudden they fly a Gulf Stream 100, which is a significantly larger plane and a very different design.