Throughout the series the team is shown being pursued around the country by a squad of Military Police (MPs). MPs have no jurisdiction or authority off a military installation, and certainly do not travel around the country chasing after suspects. The job of tracking down and arresting deserters is assigned to the FBI--not MPs.
In order to have become a Green Beret BA Baracus would have to have undergone Airborne Training and completed a number of parachute jumps. Yet according to his mother he was afraid of flying even from an early age. However, given BA's tenacity and toughness, that doesn't discount the possibility that he did many parachute jumps simply because he wanted to face that fear and overcome it. In addition, given that Murdock's flying is blamed as well for BA's fear of flying, it's likely that his phobia was exacerbated dealing with his experiences with Murdock's piloting on duty.
Throughout the series due to budget constraints, several scenes and special effects shots are lifted from well known movies from the 70s and 80s and even from earlier A-Team episodes.
Throughout the series, several actors play several different characters, with minimal attempt at disguising this.
Throughout the series, the stunt doubles used to stand in for the actors are often very obviously not the actor in question. This is consistent with other action/adventure TV shows from the same era and ilk.