When instructing Jack how to operate his parachute, the leader of the Flying Elvises (Utah chapter) tells Jack to pull the yellow lever. He then tells him if his chute doesn't open, he is to pull the red lever to activate the reserve chute. After Jack jumps, he pulls the yellow lever and then immediately pulls the red. According to the Flying Elvises leader, this should have activated both parachutes.
In the card game in hotel room, one player gets up to leave. In the next shot, he is still playing.
When Jack is on the plane with the Flying Elvises and learning how to use the parachute, it is daylight outside as seen through the windows of the plane and the interior of the cabin is full daylight. When they get up to jump, just minutes later by the film's time line, it is completely dark outside and the cabin lights are on inside the plane.
When Tommy is watching Betsy at the check-in counter they are standing next to the Indian Elvises who are also checking in. A split second later the Indians are walking past them as if they have already completed check-in or never checked in.
When learning the parachute, Jack is told to pull the yellow handle for his main chute and if that didn't open, to pull the red handle for the auxiliary chute. He ends up pulling "Yellow then Red" which would deploy both chutes. Having both chutes deployed would be dangerous and impossible to control.
When the little Elvis is singing in the lounge, his mouth does not move with the soundtrack and at times turns away from the mic and his voice remains at the same volume.