Optimus, known as Nemesis Prime under control of Quintessa, regains control of himself once he hears Bumblebee speaking with his true voice. Prime claims that he hasn't heard Bee's voice since Cybertron. However, Bumblebee used his true voice at the end of the first movie, while still on Earth.
Daytrader brings Starscream's head to the junkyard, and Megatron is later seen holding it when he and his Decepticons arrive. However, the head here is fully intact, when in Transformers: Dark of the Moon, Starscream lost his eye and his head was blown apart by Sam.
We see Merlin drinking out of a glass bottle with a grooved neck that is clearly for a screw on cap. That's at least a few hundred years ahead of its time.
When Cybertron is approaching Earth, a scientist from the European Space Agency states that the International Space Station will be hit by the planet and that it has no escape pod. This is inaccurate as the International Space Station has a one or two Russian made Soyuz spacecraft docked during an expedition depending on how many astronauts are on board. So in reality, the astronauts would have been able to escape and avoid certain death from collision between Cybertron and the International Space Station.
When Vivian comes home with Cade, the first shot where you can see the mirror in the back, shows the cameraman bending over his own camera.
Even though the Battle of Chicago occurred in Dark Of The Moon (2011) in Age Of Extinction (2014) Chicago has been restored to the way it was before the battle but now seems to be back to a post battle wasteland.
Optimus arrives at Cybertron and is distressed, asking "what happened to [Cybertron]?" However the fate of the planet in Dark of the Moon  would have been clearly visible to Prime back on Earth.
The Royal Navy's Submarine Museum is actually nowhere near London as the movie depicts, it is actually in Gosport, near Portsmouth, in Hampshire.
In one scene, Cade breaks open the glass of the dying Knight's ship, completely opening it up. In a shot later on, the glass is intact.
When Vivian is kidnapped by Hot Rod, she is wearing heels. When Hot Rod spits her out of the car at Burton's castle, she is wearing tennis shoes.
When Daytrader brings a new voice box for Bumblebee, he lies on his back like a patient at the dentist while Cade and Izabella fix it for him. In several shots, Bumblebee's head is clearly a prop as the rest of his body has disappeared behind Cade and Izabella.
When Bumblebee and Optimus are fighting on top of the alien ship, Cade's shirt is torn around the neckline and the arm. After Cade saves Optimus from the Knights, his shirt is no longer torn.
Stonehenge as shown is not as isolated in open countryside and from main roads as portrayed - the A303 among other roads runs past the monument and also the town of Amesbury is across said main road less than two miles away.
When Cybertron scrapes the surface of the Moon, the landing site of the Apollo 11 Lunar Module is shown with the American flag still standing. This is wrong as the flag was blown over when Apollo 11 lifted off from the surface due to it being planted to close to the Lunar Module. Future flags were planted further away during the other Apollo missions to prevent this from occurring again.
Towards the end of the movie Colonel Lennox states that the Osprey's flight ceiling is 12,000 ft and the target where the battle will be taking place is at 21,000 ft, "nearly double" and the air would be too thin for the Osprey's rotors to "bite". This is incorrect. The Osprey's operational flight ceiling is in fact 25,000 ft, well within the operational area.
When we first see the Samurai Autobot "Drift" in the junkyard he is balancing on his sword on the roof of a car causing no damage apart from a few scrapes. However the sword alone would have been heavy enough to at least dent the roof, adding the weight of Drift would have caused him to skewer the car like a kebab.
Hopkins is shown running down St Helens Passage in Oxford to get to the library. Not only does that mean he's running away from the library, he's also going down a dead-end that leads to only one thing - a pub (the sign for which is clearly visible).
A statue of Optimus from ancient history is shown in Sir Edmund's office. The design used for Optimus here is clearly his knight armor that he wears in this film, despite the fact that he did not look like this until the fourth installment.
at 51:45 into the movie the talisman that the knight gave cade attaches itself to his right arm at the bottom of the rolled up sleeve. We see that arm several times over the next several minutes including a very nice view at 52:58 and again at 53:45 the talisman is not there.
When bumblebee shoots the decepticon police car in London, driving past a side road, you can see a normal police car next to a regular car waiting, but in the close up of the decepticon crashing/blowing up on to that street the cars have changed.
In Dark of the Moon, We can clearly see that Cybertron is much larger than Earth but in this movie it is only about a third or half the size of Earth.
Submarine is in London then in the next shot appears to be leaving Dover harbour.
In 2:12:34-2:12:36, a cameraman can be seen right behind Mark Wahlberg and the cast as the camera pans up towards the ignition chamber.
The library in Oxford that is shown several times is not called "Trinity Library", it's The Bodleian. Trinity is a college.
Most of the streets used in the Oxford driving scenes (particularly around the Bodleian and Radcliffe) are pedestrianised.