After the original Trees Lounge shut down, Steve Buscemi bought the sign and restored it to use for him movie, although he was not able to use it. He then gave it to a woman who worked at Trees Lounge for 40 years.
During the wake, when Tommy and Debbie are praying over Uncle Al's body, you can see Seymour breathing, even though he is suppose to be a dead body in a casket.
When Tommy reminds Debbie to collect her bag when he is dropping her off, you can see a crew person in corner of screen as well as in the window reflection.
During the opening credits, an old man at the bar orders a large glass of liquor, filled with ice. In the next shot, there's no ice in the glass. However, this is a deliberate technique by the director to indicate the passing of time at Trees Lounge.