When Roy and Frank return to the house and find that Angela is missing, Roy is caught by Frank walking on his own carpet with his shoes on. The sound of him turning on the carpet is the sound of a wood floor not carpet.
Roy Waller purchases Tareyton cigarettes, and is seen with packs of Tareyton, but smokes Kool cigarettes throughout the movie. The name can be seen on the cigarettes, and the telltale Kool gold stripe is seen on all his smokes. The ashtray in Roy's car in one fast cut shot is also full of Kool butts.
When Roy is telling Angela he doesn't want her around, she unwraps the puppy angel ashtray and reaches into the car. But when she sets it on the dashboard the ashtray is still wrapped, Roy then picks it up and unwraps it again.
After pulling the things from the pool to dispose of them, Roy goes to take his pills, puts them on the counter and reaches for a paper towel. When he gets the paper towel, the pills aren't on the counter. Then in the next shot they are back.
When Roy is sitting in his car waiting to meet Angela and about to give up and drive away, he has a cigarette in his mouth as seen through the windshield. In the next shot, as he is about to turn the keys to the ignition, he's holding the cigarette in his hand.
When Roy Walker plays the second side of the vinyl record: Frank Sinatra's Greatest Hits! (Reprise Records 1968) the needle is placed on the fourth track which lists the song "When Somebody Loves You" (written by Sammy Cahn and Jimmy Van Heusen). The song that plays out of the speakers though is the fifth one on the same side which is "This Town" (a legendary song written by Lee Hazlewood)
Despite the fact that obsessive-compulsive Roy has supposedly been locked in his house for days cleaning every square inch, dirty fingerprints are clearly visible on the door when he finally answers it.
When Roy, Frank, and Chuck are having lunch... Roy tells Frank he's got to fly to Phoenix. Chuck is holding his wine glass by the stem, and in next camera view over his right shoulder, he's holding it by the globe.
The goof item below may give away important plot points.
First, given the fact that Roy never met Angela, there is no possible way he could have assumed that Angela was his daughter. Roy has OCD and Tourette Syndrome, but he is not delusional. Secondly, realistically, Roy should have contacted Heather, his ex wife to talk about their "daughter." Or at least left a message. Lastly, what would have happened if Roy didn't notice Angela and continued driving?