Before Woody jumps out of the plane, he's wearing a plain yellow jumpsuit. When he's seen falling away from the plane, he's wearing a striped jumpsuit like Cliff's.
It is not legal for beginners to free fall (jump from the airplane without the rip cord line being attached to the airplane) on their first jump. In fact, people must complete dozens of attached line jumps before being allowed to do their first free fall.
Norm jumped from the plane much later than Sam, so there would have been no way for the two of them to hold the Cheers banner together during their descent.
When Sam reads the suggestion to Rebecca about Cheers having a Happy Hour, Rebecca replies with, "Not legal in the State of Massachusetts." Massachusetts is known officially (and in all legal references) as the Commonwealth of Massachusetts.
The yokes in the aircraft cockpit are not correct for the model aircraft shown in the exteriors.
When Sam is reading the suggestion for a Happy Hour, Rebecca says it's not legal in Massachusetts. In The Tortelli Tort (1982), Sam says "Happy Hour is over," when Big Eddie says he is going to sue Sam for Carla's violent outburst. It seems like a mistake, but during the six intervening years, Massachusetts outlawed happy hours in real life.
During the skydiving shot, George Wendt is replaced by a stunt double who is obviously much thinner.
After Norm, Cliff and Woody chicken out the first time and Carla is grilling Woody, he's sitting on the bar telling his rehearsed lie and over his shoulder you can see an extra standing outside the Cheers door waiting for his cue to enter the bar.
As the men exit the airplane, their jumpsuits show absolutely no wind effects.
In the final TV broadcast showing the guys jumping with the Cheers banner, the landscape below the jumpers, with its deserts and mountains, is clearly not Boston or New England but Southern California.