Dan and Beth's phone number is clearly visible on the phone when Alex calls him the morning after their night together 316-6752. Later in the movie Alex calls information to see why his phone number can't be reached and quotes it as 212-555-8129.
When Dan speaks to Beth about Ellen missing school, Beth says "She's only five years old. What's she going to miss, trigonometry?" While eating dinner at Alex's house later that same day, Dan tells Alex that he's "got a six year old girl".
When Dan breaks into Alex's apartment, he sees a newspaper clipping about the death of Alex's father, Stanley Forest (with one r). However, Alex's last name as listed in the credits is Forrest (with two r's).
The newspaper clipping about Stanley Forest's death was from 1959. Alex had mentioned that her dad died when she was 7 and at another point says that she is now 36 years old. Based on dates on the unused opera tickets, we see that it is 1986, putting her birth year at 1950. Thus, she would have been 9 years old in 1959, not 7 years old. Also, the clipping says that Mr. Forest was 42 when he died, but the man in the photo appears to be around 60 years old.
Immediately after their first date at the restaurant, where Alex tells Dan that they're "we're two adults," the scene immediately shifts to Alex's apartment where she and Dan are heavily involved. They later go dancing and when they return to her place, Dan asks, "Do you live here?" (or something similar). Why is he surprised when he just spent the night with her there?
When Dan is getting dressed after having sex, Alex is still in bed and her breasts are exposed. Then the covers are up to her neck, back to the foot of the bed, and then to the side where she's once more covered.
Dan listens to Alex's tape during the ride home and when he arrives there. In the later sequence when he's listening, these parts of her tape are almost at the same time. This is impossible due to Dan's location when he listened to both parts.
In the scene where Dan Gallagher is driving to Alex's apartment to confront her about taking his daughter Ellen, he is in traffic, in the left lane, with a car directly parallel to him in the next lane on the right. When he switches lanes,the car that was in the lane he was getting into has suddenly disappeared, and a car a short distance away can be seen in the same lane.
When Alex is following Dan home, she is in the car directly behind him. This is shot in parallel editing, so when we see his face in the reaction shot, her car should be directly behind him. It isn't. Where was she?
During the climax scene as Alex was talking to Beth, we see her scratch her dress with the knife she was holding and then blood starts dripping to her right foot. Alex's right foot was clean and had no mud on it. However when Dan drowns her in the bathtub, we see mud on her right foot. How did she suddenly get mud on her foot?
The tape recording that Dan listens to in his study is different than the one he listens to in his car. Alex's tone of voice is different, and additional talking is added. Also, it is impossible for Dan to put the tape in the cassette and listening to the same things she says without rewinding the tape first.
Alex slits her wrists after she gets angry with Dan. Later on, when she goes to meet with Beth about buying the apartment, she has a wristwatch on one arm and a set of bracelets on the other. However, in a shot before Beth gives Alex their phone number, the bracelets fall farther down Alex's arm, and you can see that her wrist is smooth without any scarring.
Before the final scene, there is an outside shot of the Gallagher home. It is supposed to be late Fall (Christmas decorations seen while Beth is driving, Ellen practicing for her Thanksgiving play) yet the trees outside the home are all in full bloom.
The goof items below may give away important plot points.
When Dan and Alex are having sex in the elevator, they are first standing on the side closest to the windows, and then they move to the other side where shadows are cast from the windows. However, when we zoom in on them, they are back on the opposite side of the elevator.
In the final scene after Alex is shot and the police arrive, Dan is seen outside of his house and the front door is clearly solid white. When he walks back inside the front door is still white but there is a large stain glass window on the door.
Near the climax, a loud, violent struggle occurs in the bathroom and screams for help are shrieked. The struggle ends with a loud gunshot. Ellen is asleep down the hall in her room and does not once come out, alarmed or worried about what's happening.