When Isaac asks Tracy how old he will be when she is thirty-six, she says "sixty-three," and he agrees. Earlier Isaac says that she is seventeen and he is forty-two, which means he is 25 years older than her, and would therefore be sixty-one, not sixty-three.
Mary (Diane Keaton) is supposed to be an intellectual, but when she says the name Diane Arbus, she mispronounces it, saying "Diane" the same way you would say Diane Keaton. Diane Arbus' first name is pronounced "Dee-Ann".
During the fireworks in the opening sequence the screen goes black several times - but not completely: Two bright circles - glasses - can be seen as a reflection (probably because the sequence was filmed from behind a window) and there is also a very slight after-image of the person wearing the glasses who might even be the director.
In the first scene at Elaine's, as Isaac is beginning to say something, someone (presumably a customer of the restaurant, as it was running while they were shooting) walks in front of the camera. Isaac laughs, and quickly recovers with an impromptu remark about how his girlfriend has to go and do homework.
The goof item below may give away important plot points.
In the final scene, when the chauffeur takes Tracy's bags out of her building, we can see (via reflection) that he leaves the glass front door open. When we cut 180 degrees back to Isaac, the door is still closed.