(at around 1h 8 mins) When Newt is trying to describe the physiology of the Kaiju he likens their two-brain biology to dinosaurs. However, the theory that dinosaurs had two brains was abandoned decades ago.
(at around 1h 35 mins) When Marshall is talking with Raleigh about the Mark I Jaegar's radiation affecting him, he turns around from a mirror to wipe his face with a towel. In the next shot, he his significantly farther away from the mirror than he should be, causing him to throw the towel at the mirror.
(at around 55 mins) After Mako's first drift test, Raleigh goes over to help her as she's coming out of it, there is no suit material covering her neck as she's standing. When Raleigh helps Mako to sit in the Conn-Podd her neck is covered with the suit fabric.
During the final mission to close the breach, Newt and Gottlieb rush in saying they can only enter the breach with a kaiju since they have some sort of genetic code that grants them passage. Yet when Mako and later Raleigh eject from the Gipsy danger they can pass trough the breach without a kaiju ''code''.
(at around 44 mins) When Newton is preparing for his first drift with the kaiju brain, he places the headpiece on his head. In the next shot, the collar of the headpiece has fastened around his neck without him touching it.
The scene with the Kaiju breaking through the wall in Sydney makes no sense. Given that the opera house is on the seaward side of the harbour bridge it would have had to be breaking through from the land side of the bridge. If it is already on that side it does not need to break through the wall.
Throughout the movie, the control team members erroneously refer to enemy targets as "bogeys". A bogey is an unidentified target; once it has been identified as hostile, then it is referred to as a "bandit."
(at around 20 mins) When the Kaiju breaches the sea wall and is threatening Sydney, it is first shown striding under the Harbour Bridge, towards the Opera House. Travelling in this direction, the Kaiju would actually be heading towards the ocean, not coming from it.
As the final attack on the breach commences, at 1:46:00, Pentecost informs Chuck that the breach is 3000 meters down. Chuck responds "Half a mile!? I can't see a bloody inch" 3000 meters is close to two miles. It is also odd that someone with an Aussie accent would refer to imperial distances, especially in times of stress.
When one of the Jaeger is shown to go supersonic, one can see the plume when it goes supersonic. However, the boom isn't a single event. It should keep manifesting itself all along the path of that Jaeger.
Note that the walking paces of the jaegers do not match the walking paces of the pilots, appearing significantly slower than the pilots' movements, even though the pilots are directly controlling the jaeger movements synchronously.
(at around 1h 14 mins) Gipsy Danger is said to be immune to an EMP because it is "nuclear powered" and therefore "analog". This would be nearly impossible as the two have nothing to do with one another. Most nuclear reactors have many digital parts and computers controlling them. Furthermore, the cockpit of Gipsy Danger is filled with what appear to be digital computers.
When the kaiju emits the EMP, it takes out the jagers, the command center, and presumably anything that's digital. But when the Gypsy Dancer attacks, it is carried by a fleet of helicopters, which presumably have the same digital circuits.
At various points in the movie in the control room. When members communicate to the Jaeger pilots via the microphone, they do not press the black button on the mic. The Shure gooseneck 515 series microphone requires that the black button is pressed in order to transmit. Therefore, the times characters speak into the mic without pressing the button would result in no voice transmission.
CGI Blood: When Mako points out to Marshall Pentecost that his nose is bleeding, the blood drips from his nose to the top of his shirt collar, despite the collar being under his chin. The blood should have fallen onto his shirt front.