(at around 2h 30 mins) In the Optimus/Lockdown fight when Cade hides behind the wall and Lockdown fires a round into the bit of wall right next to Cade all of a sudden someone in a grey suit is visible behind that wall for less than a second who instantly bursts into a cloud of red mist. He wasn't there in the shot before and no trace of him whatsoever can be seen afterwards.
(at around 41 mins) When the main characters are being chased through the cornfield by the CIA, a pursuing car hits them on the side, however in the next shot the car has disappeared and the main characters car has not lost any speed.
(at around 1h 21 mins) When Tessa gets into the white car that Optimus is laying on, she shuts the door. The camera changes a couple times. When it shows Optimus from the outside, the door is open, and when it pans back to Tessa, the door is closed again.
(at around 9 mins) When Optimus is being towed to Cade's property, there is a shot of Cade turning on to the road leading up to his house with the sun is setting in the backdrop. The next shot of him arriving at the house still towing Optimus it appears to be midday.
(at around 1h 35 mins) When Tessa is climbing along the rope, the dogs are shown climbing behind her in one shot, and then are gone in the next.
(at around 58 mins) At the dig site, the find was said to have been carbon dated to 65 million years. This is not possible, because carbon dating does not work on samples this old. Also the sample was said to be metal, which can't be carbon dated regardless of age.
(at around 1h 6 mins) When Bumblebee does doughnuts in the KSI building, one of the villains states that the they "Don't scan collector car junk". However, there is a vintage Corvette stingray race car seen just prior to this. So obviously they do scan collector car junk.
(at around 2h 35 mins) A Mercedes-Benz police van representing the Hong Kong Police SWAT (HKP-SWAT) can be seen at Victoria Harbour where the Autobots gather with the police. The tactical unit of HKG is in fact known as the Special Duties Unit (SDU) and have always being plain navy blue with simple "POLICE" marking and use a Mercedes-Benz Unimog U5000 for armored personnel carrier, not a 814D. Due to their secretive nature, unlike other tactical units, they never carry out operations without wearing balaclavas.
In Hong Kong during the chase between Yaeger and Savoy, Savoy drops what looks to be a split-type air-conditioner unit down to Yaeger but it somehow looked to be mounted outside of the wall not through the wall, as there is no hole in the wall.
When Cade first stumbles upon Optimus in the theater, he opens the door and a bunch of large caliber shell casings fall out. Cade then mutters "Mortar Shells?" Yet in his hand is the casing shell for what appears by size to be a 40mm BOFORS Anti-Aircraft Shell, the largest shell appears to be a 105mm. Neither of which are Mortars by type of munition.
(at around 36 mins) When Shane first drives and parks by the ranch fence (when the military is interrogating the Yeagers), there appears to be no one in the car.
(at around 15 mins) During the fight on the boat near the beginning of the movie, the covert ops team commander is watching the action on his monitors. Many of the monitors are green indicating they will have content added in post-production. There is no logical reason for them to be green, they would either be off, on with images, or on a standby mode. The content was never added. We see this a few times.
(at around 2h) Obvious stunt double for Bingbing Li when she crashes the bike during the chase in Hong Kong (sneakers vs high heels).
(at around 1h 18 mins) Several times the human characters fall or are thrown several feet without any injuries. During the highway chase scene where Prime fights Galvatron for the first time, Tessa rolls along the concrete highway at highway speeds but then gets up without a scratch. During this same scene, the humans are thrown in the air through fire and "caught" by metal robots without a scratch.
(at around 2h 5 mins) During the fight/chase along the rooftops and down the side of buildings in Hong Kong an air conditioner unit is pulled off the wall and dropped on Cade. The wall was left completely blank showing that it was not a real unit as there was no window or any access through the wall for air to flow nor were there any wires or piping.
(at around 1 min) One dinosaur that's shown witnessing the great extinction event at the end of the Cretaceous is a Psittacosaurus. Psittacosaurus went extinct in the middle of the Cretaceous, around 40 million years before the end of the age of dinosaurs.
(at around 1h 28 mins) During the pan shot of the autobots preparing to board Lockdown's ship, Crosshairs' mouth is clearly moving, but no words are coming out.
(at around 1h 55 mins) When a KSI scientist transforms a My Little Pony doll into a gun, the doll squeaks. My Little Pony dolls do not squeak.
(at around 53 mins) During the Autobot arrival scene in Monument Valley, a white pickup truck can be seen in the reflection of Optimus' bumper as his truck turns toward the camera.
(at around 2h 30 mins) The shadow of the action camera is visible on the truck wheel.
(at around 1h 15 mins) During the Galvatron car chase, the camera crane is briefly reflected on Stinger.
(at around 1h 55 mins) All of the vehicles see in Hong Kong are left hand drive. In Hong Kong they drive on the left and so most vehicles would be right hand drive.
(at around 1h 55 mins) In China, the main characters drive from Beijing to Hong Kong in one evening. The two cities are 1,504 miles apart (source: Bing Maps). It would take 22 hours to drive that distance by car (including traffic).
(at around 2h 25 mins) In many scenes on Hong Kong island, characters talk about reaching "the bridge" to escape, but the main Hong Kong island is not connected to the continent by any bridge, only tunnels. The large bridge featured later in the movie connects the continent to another island (Lantau).
(at around 2h 10 mins) In one of the fight scenes in Hong Kong, an Amercian-style yellow traffic light is hanging by wires. Hong Kong, being an ex British colony, used and continue to use United Kingdom-style traffic lights.
The fight scenes in Hong Kong jump all over the place. In one scene Optimus Prime is fighting simultaneously in different parts of Hong Kong Island (Causeway Bay, Central and Admiralty) and also Kowloon, on the other side of Victoria Harbour.
(at around 2h 5 mins) In Hong Kong, when Cade, Joshua, Tessa, and Shane enter the elevator to run away from the rooftop, the elevator won't move and Cade says it is overloaded. But in the next scene, we could see that the maximum amount of person that the elevator could bring is 9 people. There are only 4 people and the seed (the seed is not as heavy as human because Joshua could lift it easily).
(at around 36 mins) When the CIA is looking for Prime on the Yeager farm, a 30+ foot hole under the barn becomes available for Prime to hide in and even though the CIA team has technology to see through walls as demonstrated earlier in the movie when they capture the Autobot on the riverboat, they cannot detect Prime through a few wooden slates that are spaced enough to see through with the naked eye.
In previous installments, Energon detection was supposed to be the way Transformers could be easily tracked and spotted, yet in multiple instances in this movie the technology seems to have been lost: by the squad team in the barn where Prime was being repaired, or earlier when Lockdown is obviously using infrared vision to track Ratchet.
(at around 1h 17 mins) When Galvatron and Optimus fight, Optimus and Bumblebee save the people, and then Optimus and Galvatron resume fighting. The other Autobots should join the fight, but they are not anywhere near.
(at around 1h 3 mins) Somehow, taking a picture of a random employees badge gives Cade unrestricted access to the entire KSI building including the Top Secret labs and access to the head of the company and top scientists. There is no way that a picture of the front of a card would give swipe access to any areas as the access is coded on a strip or chip in the card and is not visible.
(at around 49 mins) Shane says that the Romeo and Juliet law protecting his and Tessa's relationship states that they can be together as they were already together when Shane was a minor. This is only partially correct. Shane has a legitimate defense against "Sexual Assault" (Sec. 22.011) as Tessa has consented and is over the age of 17, and when they were dating when he was 17 and she was 14 there is an age difference of less than three years (provided Tessa turns 15 before Shane turns 18). However, the issue of their age difference, consent, prior relationship, and Tessa being 17 only applies to the crime of Sexual Assault. Romeo and Juliet laws do not protect him from the crime of "Sexual Performance by a Child" (Sec. 43.25) for engaging in "sexual contact, actual or simulated sexual intercourse" with Tessa. Here the relevant age to engage in sexual conduct is 18 (she is 17), and the difference in age must be less than 2 years (there's 3) for a legitimate defense against the crime.
(at around 6 mins) When Cade first opens the door to the truck (Optimus Prime), he looks at the bullet casings that fall out and identifies them as "Mortar shells?" Mortar shells do not leave behind casings, and an intact mortar shell is not that shape, nor would it be made from brass.
At approximately 02:31:00, Mark Wahlberg's character shoots the alien rifle at Lockdown after he has stabbed Optimus Prime. Upon his approach to cover, Mark Wahlberg's character is alone at a wall; however when Lockdown returns fire someone else takes the hits at the wall Walberg's character was just alone at, vaporizing him.