Audio problem: When the Mexicans begin their final attack, we see Travis call to Joe to wake him up, but if you watch closely, you don't see his lips move, you just hear "Joe."
Factual error: In reality, the chapel of the Alamo was much further back then what you saw in the movie. In fact, it didn't even border "Alamo Square", the large area of land in the middle of the surrounding buildings and walls. Instead, it had its own little square courtyard in front of it, and a small wall leading to the chapel's courtyard bordered "Alamo Square". In other words, the chapel itself was about 30 to 40 feet behind the rest of the walls and buildings.
Factual error: In the scene where Houston is in Gonzales and when Guinan rides up to him, there is a shot of soldiers in the background and you can plainly see that one of them is wearing a pair of modern, zip-fly jeans.
Factual error: The cannonball that Travis cuts the fuse off is way too big for the Mexican artillery. The largest cannon they had at the battle was an 8 pounder, meaning a ball about 4 inches wide. A cannonball as big as the one Travis carried would have been at least 100 pounds.
Other mistake: In the attack on the jacales outside the Alamo, a Mexican soldier is shot and crawling on the ground. Crockett asks him his name just as he dies. Later at the Battle of San Jacinto, the same soldier is shown sinking below the surface of Peggy's Lake as a Texican strangles another soldier with his musket.