(at around 14 mins) When Hope is driving Scott to the lab, their SUV is confronted by pigeons and one of the pigeons pecks a dent in the hood. When the SUV is brought back to full size, the dent is gone.
(at around 1h 30 mins) When Hank finds Janet, she lowers her mask so it hangs on her chest. It's gone in the next wide shot, and reappears later on.
(at around 1h 29 mins) After Scott retrieves the lab from Sonny, he walks back to shore with it, leaving Sonny knocked-out on the ferry, but after the thugs are tazed, tied up, and truth-serumed, Sonny is with them back on shore.
When Janet Van Dyne is using Scott Lang's body to assist Hank and Hope she takes Hank's hand. After she vacates and Scott returns to consciousness he puts his hands on his hip.After a cut Scott lifts his hand up in confusion showing that he is once again holding Hank's hand.
(at around 48 minutes) When Cassie calls her Dad, Bill Foster pushes the answer button then lowers his right hand but in the next shot, over Scott's shoulder, Foster's right hand is still on the phone.
When cars change size during chase, their speed is unaffected. This is inaccurate as their wheels are now much smaller but keep their angular speed which is determined by the engine. So, linear speed is greatly reduced; as much as the radius of the wheels.
Some scenes in the film take place in San Francisco, California and when police vehicles have their emergency lights on, they are missing a steady red light. According to the California Vehicle Code, all law enforcement and emergency vehicles are required to display at least one steady red light in the front of the vehicle when the emergency lights are on.
Throughout the movie the lab is shrunk and moved, it is also moved haphazardly yet when the building is enlarged again at a new location, it automatically has electricity, plumbing, and nothing seems out of place when it was pretty much in an earthquake. However we are given explanations for these in the movie. Firstly, the lab is entirely self contained, and powered by the giant AA batteries we see. Second, they arm "gyroscopic stabilizers" before they shrink the lab, to protect its contents.
The Wasp's "suit" is RED when she initially enters the quantum zone after shrinking to fit between the molecules to deactivate the missile. When Hank Pym rescues her, she has on a shirt of some sort covering her torso, but it looks as if the suit is BLACK. If observed closely once Hank and Janet are leaving the Quantum Realm it is shown that there is a city with buildings in the realm showing there are beings who live there. It was also confirmed by the director there are civilizations in the Quantum Realm. This is probably where Janet not only had food and shelter but where she received new clothes.
(at around 1h 21 mins) When Hank Pym is travelling into the Quantum Realm, his vehicle temporarily pauses at the microscopic level to get its bearings. He is surrounded (and nearly eaten) by floating tardigrades, a very resilient microscopic creature. Tardigrades natural habitat is in water, yet there is no indication that he has traveled into water, unless one considers the prevalence of exhalation-droplets from respiration of anyone who has been inside the building up to this point.
(at around 1h 19mins) When the Mercedes van is being chased down the streets of San Francisco, there are two cuts that are clearly sped up: people on the side pavements move comically fast if one pays attention to them instead of to the vehicles taking part in the pursuit.
(at around 16 mins) When Hope and Scott are exiting the elevator, the floor button stays lit.
Sonny Birch's "southern accent" tends to "phase out" during times of stress.
You can often see the white bounce board (for reflecting light onto faces) in the reflection in Hank's glasses throughout the movie.
(at around 23 mins) You can see the reflection of a boom pole in the lamp during Sonny and Hope's first talk, right after Hope sits down.
Throughout the movie, as in Ant-Man, the mass (weight) of the objects which shrink and enlarge is never handled consistently. Sometimes objects (such as the people) retain their full weight when made very small, hence able to affect much larger objects with great force. But the same is not true when large heavy objects like cars and buildings are made small. Also, when Scott becomes very large, his mass is proportional to that, instead of remaining his actual ~200 lbs.
Janet should not have aged in the Quantum Realm, it is stated many times that time doesn't pass there, meaning she should still be around 30 years old.