When Michael steals a jeep from the secret defense facility and trades it for another vehicle, the number on the hood of the jeep he stole is different than the number on the jeep he trades.
The chase through Madison Square Garden is supposed to happen in the summer of 1981, but the circus poster says the circus shows started Wednesday the 1st and ended Sunday the 31st. The only 1981 dates that correspond are April 1st to May 31st, which dates are all in the Spring. Also, the newspaper Pruitt was reading in the club was dated in August 1981.
When Michael uses the Sony remote to change the channel on the Sony TV in Nathan's bedroom, the channel number doesn't change. In 1981, there could have been a cable box, but none was visible and Michael was holding the TV remote, not a cable remote.
The police car that cruises past the cab company office in the Hell's Kitchen neighborhood is from a Bronx precinct (over 15 miles away).