The model of the space shuttle includes a rust colored external fuel tank. In the early flights of the space shuttle the tank was painted white. Most likely if any models existed during development of the shuttle they would have had the tank painted white.
At the end of the movie, the narrator explains that Hayley grew up to be a supermodel and a pitcher on the Olympic softball team. Women's softball did not become an Olympic sport until 1996. Hayley would have been around 35 years old in 1996, a very unlikely age for an Olympic softball player.
At the first encounter over the sandlot field, when Mack states "Are you deaf?" to Samantha, he turns and apologizes to Fingers. Since Fingers is deaf, and Mack was not facing him, there is no way Fingers could know what he said.
When the boys arrive to see Smalls on the sandlot for the first time, and they all charge toward him on their bikes, Fingers is seen getting off his seat just as they charge. However, the very next shot, he is back on his seat.
When The Great Fear's chain is welded to a Battleship anchor, the anchor is huge, larger than the person welding it. When you see the anchor in all the shots afterwards, where the kids try to get the model, the anchor is tiny about 20% the size of the one welded on in the beginning.