After destroying Paul's car, in the following scenes in the parking lot, the car appears whole and undamaged.
In the beginning of the film, Adam Sandler tells his daughter to put the Mets game on the car radio. He says he splurged and got satellite. The movie is set in NYC so it's available on regular radio.
While Danny is on the phone with Eliza (who is at Bard College), he states, "I might go stay at Jean's in Rochester for a while. I'll be closer to you...". The distance between Rochester and Bard College is actually significantly greater than New York City to Bard.