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.
When Taron Egerton (Eggsy) and Mark Strong (Merlin) are at the end of the Statesman bottle of whiskey and have nearly drank it all, they notice the bottle has been marked "Distilled in Kentucky." When Merlin then makes a reference to country western music he starts to then sing the beginning lyrics to "Country Roads" written by John Denver. John Denver wrote the song "Country Roads" about the state of West Virginia and the lyrics of the song itself make several references to West Virginia, not Kentucky.
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.
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.