Continuity mistake: In the scene where Sam meets Dylan for the first time, the distance between Sam and Carly keeps changing.
Continuity mistake: *Spoiler* After Cybertron is pulled into Earth's orbit, they show that it can be seen from the earth's surface, pretty much the entire sky is taken up with Cybertron. However, in several scenes afterwards the sky is shown in the background as being crystal clear again.
Continuity mistake: In the scene where Sam, Carly and others slide down the collapsing building, the shot from above reveals only one window hole where they could have jumped from, and Sam and Carly are sliding quite far off to the side from the hole.
Continuity mistake: In the highway chase scene, one of the Decepticons knocks down the freeway sign which causes the signs, originally facing the on coming cars, to flip away from them. The other two Decpticons then use the signs to as a ramp to get further down the road. This should be impossible because the signs didn't land that way. When the Decepticons land, the signs are pointing the first way again.
Revealing mistake: Right after Sentinel finishes his speech at the tower, there is a shot where a lot of ships are shooting at buildings, but when they smoke from the explosions is gone, none of them is damaged. This mistake can also be seen when the dropped US soldiers are being chased and shot at by Decepticon ships.
Continuity mistake: Towards the end of the movie, when Dylan is pointing a gun at Sam, he has both hands on the gun. In shots of Sam, one of his hands is on his side.
Factual error: Neil Armstrong's first step onto the moon as depicted in this film is incorrect. In real life he descended the LM ladder until he was standing on top of the little dish at the end of the landing leg. He then jumped back onto the ladder (the lower rung of which was a few feet up) to see if he could climb back up. He then jumped back down to the LM footpad. Then he stepped off into the dust to create the first footprint on the moon. The film shows him climbing down to the lower rung of the ladder, then just jumping into the dust where the initial footprint is immediately trampled by his movements.
Factual error: Big Joe has an AT-4 rocket launcher, which gets loaded before he wants to shoot the pillar. AT-4's are not reloadable.
Continuity mistake: Towards the end of the film Carly is holding Sam, in some shots she has dirty hands in front of his shoulders and in other shots she has clean hands that are over his shoulder.
Visible crew/equipment: During Sam's first meeting with Bruce, at one point, there is a reflection in the ornament on the left side of the desk that shows a large black mass moving in the same direction as the shot is moving.
Revealing mistake: When Megatron blasts the Lincoln statue and sits in his throne there is a CG mistake. His left foot is embedded in the stonework with one of the wheels (only 3/4 is visible).
Factual error: While trapped in the toppling building, our heroes use bundles of computer cabling to keep themselves from sliding out. While bundles of cable are common around the US, they are against code in Chicago, which requires them to be in conduit in a plenum ceiling. Conduits would have easily prevented the bundles from crashing through an acoustic ceiling. And yes, that is a plenum building.
Plot hole: The film tries to claim that all six lunar missions were to collect samples from the Ark. However, the missions had landing coordinates hundreds of miles apart. If only 35 people knew about the secret mission, that leaves hundreds of thousands of others who believed they were working toward actual lunar exploration, meaning it would be very difficult to fake telemetry data without someone noticing. Also, there are long range photographs of the different landing sites showing the landing craft at their true lunar landing spots.
Revealing mistake: When Optimus returns from the dead, he says: "We will kill them all.". The same footage is used when he makes his speech with: "your leaders will now understand", only it's cut slightly shorter.
Continuity mistake: When the Autobots return from their fake deaths, Optimus shoots down an enemy ship by destroying the right turbine, making it crash down and saving Sam. But later on, Bumblebee starts it up and flies it with no apparent damage.
Revealing mistake: Toward the end, when Sam is going to destroy the tower he gets kicked in the stomach by Dylan. When Sam falls he lands on another part of the destroyed building, you see the chunk of building that he lands on conforms to his body, showing that it is made of foam to soften his landing.
Continuity mistake: Just before Optimus Prime arrives in the street where he kills ten Decepticons in twenty seconds, there is a shot of Sentinel saying "It's our world now!", and he is looking out over that same street. When Sam comes out of cover to take a look at Cybertron, Sentinel is still on the building. But when Sam shouts "Optimus!" Sentinel is gone.
Factual error: In the beginning of the movie, the wrong year Lincoln Continental is shown. JFK was still alive and was assassinated in a presidential 1961 Lincoln Continental, but the one that pulls up to the white house is a 1965.
Continuity mistake: In the scene when the characters are sliding down the glass building, just before they shoot the windows, there is a shot where a chair is sliding down along them on the left side. The camera dips down for a moment, and when it goes back up, the chair is gone, even though there is no hole in the building for it to go.
Continuity mistake: When Charlotte Mearing, the United States Director of National Intelligence is talking to Optimus Prime about the teleportation device, the position of her hands on the red hand rail differs between shots.
Answer: Mudflap and Skids (the two idiot robots I believe you are talking about) were removed from the film due to negative fan reaction. While we don't hear what happened to them in the context of the plot, no reason not to assume they were killed in fighting between the movies. Arcee and Chromia (2 of the motocycles) were killed in the last film.