In the Jett Rink Airport opening day parade, there are riders on horseback carrying an American flag, and a Texas flag. The American flag being carried has 37 stars (should have been 48), and the lone star on the Texas flag is upside down (the stripes are right side up).
The newspaper shown announcing Angel Obregon's return has an article about Alfred Chester Beatty giving up his American "nationality" and becoming a British citizen. Beatty was a real person that did this in 1933. The newspaper shown is from that year when it should have been from sometime between 1941 and 1945.
After Bick takes his crying toddler son for a short ride and Leslie is helping their son off the horse, the camera moves upward revealing a boom microphone at the top of the screen. Seconds later, when Bick dismounts the horse, the mic is seen once again.
At the dinner table in Maryland, Jordan Benedict states that his ranch is 595,000 acres. Later on Leslie refers to Reata as being 500,000 square miles. An acre equals 1/640th of a square mile. The state of Texas is only 267,339 square miles, so Leslie was saying that the ranch was almost twice as big as the entire state.
When Jett is talking to the oil executives about "cracking Benedict", he is seen from behind with a cigarette in his mouth, but then is seen shortly after from the front with the cigarette in his hand.
When Leslie and her children return to Maryland for Thanksgiving, they are greeted by a green midsummer landscape. At that time of year, the leaves and grass would have already turned and the trees would be well on their way to being bare.
The newspaper announcing Angel Obregon's homecoming has an article headlined "Full-Paid Taxes Record Broken". The text of the article refers to Los Angeles county and Howard L. Byram. Byram was the Tax Collector for Los Angeles county in California. It's unlikely a story like this about LA would be in a Texas newspaper. It appears that the production used a real California newspaper and added the picture of Angel.
The large display of flags in the lobby of the home has the American flag in the wrong position. It is on the right, as we see it. However, protocol requires Old Glory is to be presented "on the flag's own right," (aka stage right) meaning our left. While this may normally be correct, the display of flags are the "Six Flags over Texas". A quick Google image search will verify that these flags are consistently displayed in the following (generally chronological order) from left to right: Spain, France, Mexico, Confederate States of America, Republic of Texas and the United States of America. As such, the display as depicted in the film is accurate.
During the confrontation between Bick and Jett in the hotel banquet hall stockroom, Bick throws a "basket" knocking over several storage shelves. The shelves start to fall before the basket actually makes contact.
In the scene where Leslie faints at the barbecue, long shots show Luz standing at a table with no one behind her. But in the close-up after Leslie faints, when Luz says, "That's what I was afraid of", there is a crowd of people in the background behind her.
When Jordan forces his son to ride his horse with him at a gallop, the child dummy is clearly slipping down out of the rider's grip as he comes to a stop. The immediate close-up has the child actor sitting perfectly erect.
When Jordy introduces his new wife Juana at the pool party, the people behind Bick and Leslie are seen applauding, even though Jordan hasn't finished his announcement yet. Also, no sound of clapping is heard.
The oil wells seen in the backgrounds of live-action shots, such as at the railroad depot, are clearly miniatures erected in the near background in an effort to give the impression of size through forced perspective. Similarly, the wells seen through the windows of indoor sets (the house and the diner, for example) are plainly painted images on false backdrops.
Juana Villalobos Benedict, Jordan III's wife, is obviously holding a doll meant to be a real child when she enters the lobby of the Emperador Hotel during the storm. She hands the doll (their child) to Dennis Hopper's character and again the size and rigidness betray that it's actually a doll and not a live child.
Near the end, Bick knocks over a shelf of wine bottles, causing a cascade of shelves knocking the next one over. The scene cuts to Jett and you can hear a large number of shelves falling over. However, when the scene cuts back to Bick exiting, there are only three shelves (with the third leaning against the wall), and the other "shelves" behind are just a set painting.