Revealing mistake: When Han shoots at Bruce Willis and the others with the Gatling gun, we see cartridges on the ground. You can tell that they are all blanks. The tip is jagged and has been closed - live ammo just has an open hole where the bullet was.
Continuity mistake: At the end when Frank brings a suitcase with a bomb on the plane where Bailey is pointing a gun at Sarah, he puts the suitcase on a table. When Frank drops his gun, the table is empty. The suitcase reappears a second later when Sarah goes to Frank.
Factual error: When they are in Costco there is music playing in the store. Costco does not play music in their stores.
Continuity mistake: When Sarah is trying to convince The Frog to help them, The Frog's glasses alternate between being worn and being in his hand from shot to shot.
Continuity mistake: When Han and his team land at Teterboro, N.J. you see part of the tail code G-MPSP on the port (left) wing when they walk away from it. After Frank and his people steal the same plane it is shown taking off, but no tail code can be seen on the port wing. (00:27:35 - 00:28:25)
Continuity mistake: Han is fully naked when he is scanned, he then gets some sort of kimono but just after that you can see that he is wearing underwear (can be seen when he is walking). (00:19:30 - 00:20:05)
Deliberate mistake: At the end during the car chase, the blue car goes under the lorry trailer. All tailors are fitted with safety side bars to stop this happening, they have been deliberately removed for the action scene.
Character mistake: On the tour boat in London, the voice on the loudspeaker says 'if you look to your right, you will see the Tower of London'. Except it's on the left, given the direction the boat is travelling. (00:53:00)
Revealing mistake: After Bailey stabs multiple people, there's no blood on the knife used at any point. (01:50:00)
Continuity mistake: In the scene at a "Russian" air base, the US troops, along with Anthony Hopkins, are surrounding and about to board a Russian made AN-12, NATO codename Cub, with US AIR FORCE painted on the side. When it subsequently takes off, the aircraft no longer has the lettering on the side and appears to be footage of an older unrelated AN-12 edited in.
Other mistake: When Katya is told that Frank was spotted in Red Square, she tells the soldier (in the English subtitles) to call out the Army - but she says, in Russian, something about Spetznaz - which Is Special Forces, not Army.
Audio problem: When Han and Frank are fighting in the hangar, Frank grabs a handgun and you can hear him chamber it. After he tosses the handgun to Han, he chambers it also, but no round can be heard hitting the ground. Nor could you hear Frank decock it.
Continuity mistake: While Frank is recovering from being drugged by Katya, Sarah goes on a spending spree, buying lots of new clothes and getting her hair styled. When they go to the bank and see Katya being taken away by police, Sarah's hair is back in its ponytail. The next scene is in England, where they meet up with Victoria, and Sarah's hair is stylish again.
Revealing mistake: Near the end it cuts to a scene where there is a small group of musicians playing classical music. In the centre is a male violinist playing but his bow is about 3 inches away from the violin.
Revealing mistake: When Han is firing the Gatling gun at Frank and Marvin, he is on one side of the street, firing across the street and through the parked cars. Frank and Marvin are lying on the ground on the sidewalk, but some of the bullets' exit holes (after shooting through the vehicles) fold inwards, when they should have bent the metal outwards. (00:49:30)
Other mistake: When Katja asks Frank where he found Sarah, Sarah answers Kansas. Actually, her apartment is east of downtown Kansas City, Missouri. In Red, the camera angle shows the Kansas City, MO sky line pointing west and pans down. (00:32:24)
Factual error: The cars that bring the Americans to the airplane carry German licence plates, nearly impossible in Russia. Also the starting code on the plate (CS) doesn't match an existing city or region. (01:18:50)
Revealing mistake: When Han is firing the chain gun at Frank and Marvin in Paris, the shell casings and links are shown. The shell casings have crimped ends which are used in blanks. (00:48:15)
Factual error: When Han is shooting at the gang with the Gatling gun, and we see the holes, they are all completely circular, even though the projectiles should have hit the surface at an angle. The holes in the cars etc. to the far right should have been oblong.
Chosen answer: Insane in the sense that he wasn't completely mentally capable? Yes. Insane in that he wanted to blow them up? No. He was heavily medicated while in care and so his ramblings and confusion are supposed to be perceived as genuine. Once he starts commenting that he is beginning to remember his past, we then assume that he realizes what his original intentions were and somehow manages to contact the other agency.
But Bailey states before he kills Katja that he was responsible for leaking the post online that Marvin saw which started the whole thing. He said he took a guard's phone to do it. I believe he was very aware and was just "playing" everyone.