The A-Team/Fridge

Fridge Brilliance

 * at the beginning of the film was sad, but it made it easier for the Team to remain inconspicuous.
 * Why did the military (it isn't clear whether it's the Air Force or the Army due to uniform fail) launch RQ-9s to shoot down the C-130? Because the plane they'd stolen carried a fully-loaded/armed light tank. Why not manned planes? Murdock broke the canopies of the fighters during takeoff.
 * Pike has several chances to kill Face and B.A., but he takes his time and gloats, missing each. This would seem to come into conflict with his disgust at the unprofessional manner in which men go about trying to kill him...until you remember Hannibal once called him a 'cartoon character'- everything Pike does, he does it to satisfy his adrenaline rush, and as soon as he gets into a good firing position, he abandons all pretense of finesse and proceeds to unleash the heaviest firepower at his disposal (he is already going guns-blazing  in Berlin, seemingly oblivious to the fact that he is doing so in the middle of a populated area or that he is about to surrounded by the police from all sides). Seems about right that he'd suddenly start monologuing as soon as he had the hero in his gunsights.
 * Murdock's quote from Braveheart is an eerily apt description of the situation the Team eventually finds itself in.
 * How did Face sneak the cuffs key into the paddy wagon at the end of the movie? It probably wasn't just a tongue that Chris gave him moments before when they were making out.
 * That was pretty much obvious since he has the key in his mouth.

Fridge Brilliance

 * Why do the A-Team never hit anyone, despite being trained soldiers? Because they're deliberately missing. They're already wanted for war crimes & breaking out of prison, adding several counts of murder to that wouldn't be a good idea.
 * In "The Beast from the Belly of a Boeing", Murdock is found sane by his doctor, who says Murdock is "just as sane as [he is]".
 * Quite a good one for The A-Team of all things - Murdock's sanity (or lack thereof) was always a point of contention. However, no matter which side of the fence you fall on, it's fairly evident the guy has genuine problems. He does "get better" over the course of the series (although quite obviously still a freewheeling maverick) with the two major crossing points being his breakthrough with Richter in "The Doctor is Out" and after the events of "The Sound of Thunder". Strange but true - watch the character development.
 * There's also the unspoken idea that they ALL came back from Vietnam damaged - BA's childhood dislike of flying became crippling aerophobia, the maverick Hannibal became a reckless adrenaline junkie - Face is pretty much the only one who came back sane.
 * I disagree. Even Face was damaged by 'Nam. He already had trust and commitment issues because of his childhood. In the Army you have to trust your comrades. Your lives--and theirs--depend on it. Face, who would have only been about 19 at the time, probably saw a lot of people he had started to become friends with die in battle or in the death camp. Suddenly those childhood trust issues got a lot worse. He became afraid to get too close to anyone for fear of losing them. And even though he trusts the other rest of the team more than anyone else, you can sometimes see him pull back a bit even from them.
 * Murdock has proven on multiple occasions that he's quite capable of busting himself out of the VA. So why does he almost always wait for Face to come and scam him out? Because it's fun. There's really no other reason for it other than that it's just more fun that way.

Fridge Horror

 * In the early Season 1 episodes of ~The A-Team~, it is established that Face, the A-Team's handsome and charming but unrepentant Con Man, was raised by Catholic priests in an orphanage after they found him when he was five years old. So you think, how did Face become a con man if he was most likely raised religious? Then you think about the tons of recent allegations against Catholic priests and then you have to wonder: why isn't Face more messed up and/or does he have any repressed memories hidden in that pretty head of his? As with the Suite Life example, this had to be unintentional, but looking back, you just can't help but wonder once you think about it...
 * Religious people can't be conmen? Have you never seen a televangelist?
 * Preacher's Kid
 * There's a saying: The Irish make good priests and horse traders (the pre-internal combustion engine equivalent to used car salesmen). The two jobs have a lot of skill overlap. Charisma and persuasion being up there. No deviant priests necessary and rather unlikely. We hear about bad priests a lot because it makes for great scandal, but they're really the exception to the rule.

Film

 * Technically, Face didn't actually escape. His with him locked inside it, so would he wind up with the same type of punishment as the rest of the guys?
 * He didn't go back, so yes, yes he will.
 * Hannibal dyes his hair from white to dark brown in order to get through the airport. In the next scene, it's back to white again. So he actually took the time to dye it back?
 * It's possible he used temporary, one-wash dye that would wash out when he took a shower, but that still makes one wonder when he found time to take a shower.
 * Him dying his hair and wearing different clothes was enough to fool airport security that he was not Hannibal. Maybe he un-dyed his hair in case Lynch got fooled, too, and wondered what the heck Liam Neeson was doing there.
 * When fakes his death, why did they send him to the crematorium with his clothes on? (Aside from the fact that it would have been hard to keep that from kicking the rating up a notch otherwise, anyway.)

Series

 * Usually the show can handwave the odd lack of help from the authorities for any given week's client with a quick line of dialog establishing them as being bought off or something, but sometimes they forget. For example, in "The Taxicab Wars," Michael Ironside's evil cab company is actively sabotaging, vandalizing, and threatening Ernie Hudson's cab company, including blowing up their cabs. This happens due to Ironside's company retaliating for...Hudson's company reporting him to the taxicab commission for drug dealing and rigging rates. The episode never addresses why Hudson cannot A) report them again or B) just call the police, thus making the A-Team's involvement rather strange.
 * "Steel" similarly featured no involvement from the authorities even though the week's villain was a construction contractor who was actually blowing up a public construction site and actively threatening a rival company from working the city's job. Presumably the city would just get the guy arrested to avoid losing any more money to him.