During the opening chase sequence, Eggsy is wearing a midnight blue suit and his attacker is wearing a lighter blue hooded sweatshirt. Eggsy is shown on the floor of the car almost falling out the door and his attacker is on top. When the film moves to a distant shot, a stunts person wearing a light blue shirt is on the bottom and another stunts person wearing a dark blue shirt is on top. This scene is out of order and would work with the previous fight close up when the characters are reversed.
While descending on out of control the ski lift, the high speed spinning of the lift would have caused it to act as a gyroscope. Rather than swinging back and forth like it was it would have stayed in a fixed position.
When out of control ski lift sequence starts, on exterior shots it is the right cabin where the sequence happens on the right track ropes, rolling on high speed when it passes over the first supporting tower from the right side. In the next exterior shots when track and hauling cables snap and onward it is the left cabin on the left track ropes on the left side of the supporting towers.
The type of ski lift on which the accident happens is an aerial tramway, it is a two cabin jig back system. While one is coming up, the other is going down the mountain, and they pass each other midway on the cable span. While in an accident sequence no second cabin is shown speeding up to the upper station when the characters are in another cabin heading towards lower station.
While ski lift accident sequence happens, after the two track ropes and single hauling rope snap this would cause the second cabin which should have been speeding up to the mountain station, also roll down on the track cables towards lower station but eventually would be stopped by the emergency brakes. The movie ignores the factual existence of the second cabin, thus making the scene technically unrealistic.
The tracking device that Eggsy plants on Clara is said to be absorbed by a mucous membrane. Eggsy is forced to resort to sexual contact for this. But there are mucous membranes in the mouth and stomach as well. Simply putting the tracker into something she would eat or drink would have done the trick.
After Whiskey put his bullwhip around Galahad Sr.'s neck in the diner, he took several steps toward Galahad Sr., but the bullwhip neither sagged lower nor retracted into the handle in came out of. This means it was clearly 100% CGI, and they just forgot to compensate for the movement.
Harry's left eye was shot and he was given a pair of glasses with the left side darkened. But at Eggsy's wedding, Harry's glasses appear to have the right side darkened. This is because the scene shows Harry and Eggsy reflected in a mirror.
Charlie's new metal arm is so strong he can throw a bowling ball through a concrete wall, but when he slams Eggsy into the ground with the same arm, Eggsy is unharmed. The minimum damage would be a broken spine.
The goof items below may give away important plot points.
In the previous movie, it's established the shocking signet ring is part of the Kingsman equipment. It would have been pretty handy for Harry against the robotic dogs, but either he doesn't have it, or forgets to use it.
The Statesmen flood Harry's room in an attempt to undo his amnesia and give him the shock that will bring his memories back. But when the water drains, the things on his desk are completely undisturbed.