When Tommy is about to leave from a visit with his grandmother, he covers the brownies she brought him with tissue paper. A second later, we see him doing the same exact thing with the same paper.
When Melanie is racing the Ferarri through downtown, a wide shot reveals that the driver is wearing a helmet. Close-ups of Melanie before and after clearly show there is nothing on her head.
When Aurora is laying on the couch, she has a blanket pulled up to her chin. In the next shot, it's at the end of the couch, not covering her at all.
Begins in 1988, and later in the movie Melanie sees an audition ad for February 29th. It was a leap year so that date is correct; however, Christmas had passed earlier (Tommy tosses Aurora's brownies to an inmate and says Merry Christmas) and before that, Aurora asked Rosie to turn on the AC in the car before they went to visit Tommy so it was obviously summertime at that point.
In a 1988 scene, it is said that Patsy's 40th birthday is coming up. She should be older than this. According to a promo on either HBO or Showtime when this film was coming out, it begins 15 years after Terms of Endearment ends. Emma died at about age 30, she and Patsy were best friends and likely the same age, so she should be closer to 45.
When the family and friends are keeping vigil at Aurora's bedside, the actor playing Bump looks straight at the camera as it's panning around the room.
The General sings a song with the lyrics "Goebells has no balls." He correctly pronounces Goebells as "Gerbels," however, for the purposes of the song, it is meant to be pronounced "Go-balls" to rhyme with "no balls."