When Harry, Eggsy and Merlin are on the Statesman plane headed to Cambodia, Merlin reveals the suits they are to wear. Just after, Eggsy is seated in a chair wearing the light grey suit, while Harry is wearing one of the two black suits. Later, when the three are in the jungle, Harry is wearing the grey suit and Eggsy the black.
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.
When Eggsy gets a FaceTime from his girlfriend, the screen on his iPhone has the green accept button, along with the red decline. Unless the phone is unlocked, the screen would have the slide to unlock screen.
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.
In the opening car chase sequence, the vehicles are shown driving on the right, as if in continental Europe, when they are supposedly close to Kingsman's tailor shop in Savile Row in London's West End.
The goof item below may give away important plot points.
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.