Jerry, George, Elaine and Kramer are riding together in a subway car which is clearly marked on the interior as a #5. However, when they step off the train, the exterior shot is of a #6 train.
Jerry states that he is heading to Coney Island Amusement Park to ride the rides. However, being that everyone is dressed in coats, it is either fall or winter, in which the amusement park would be closed for the season. It is further depicted that it is the off season in the wide shot of Coney Island in the background as the train that Jerry and the naked rider are riding pulls into the station. You can clearly see that the Wonder Wheel is devoid of the passenger cabins (which are removed at the conclusion of the each operating season).
When the OTB mugger chases Kramer on the subway, they move from a car marked as "1 South Ferry" to one marked as "4 Utica Avenue" to one marked "A 207th Avenue". These trains all run on different lines and would not be connected.
During horse race, Kramer discards his betting slips. He does not pick the betting slips back up after race. Without the betting slips he would not be able to claim his winnings.
The horse race Kramer bets on, presumably at Aqueduct or Belmont, is being called by Trevor Denman, who is the announcer for Santa Anita, near Los Angeles.
Before Kramer exits the subway car while fleeing the mugger he grabs the metal pole which bends, and stays bent. In reality subway poles are solid metal that do not bend like that.
When Kramer (Michael Richards) can't find a seat on the subway, he struggles to squeeze into a seat with a large man. Almost directly behind him there is a vacant seat he could have used.
In some shots it's evident that the subway cars that the characters are in aren't moving at all.
As Kramer flees the mugger in the subway, he runs through the same car twice as evident by the same graffiti letters " BM" next to where the lady was sitting on the left side of the subway car.