Factual error: Bowie's wife had died in 1833, and from cholera, not plague. Her two sisters actually joined Bowie in the Alamo.
Factual error: When Crockett and Bowie discover Sande's powder and weapons cache, Davy picks one up and exclaims, "Rifles!" In fact, those are smoothbore military muskets, possibly British pattern, French pattern, Spanish Model 1807, or Springfield Model 1822, and only the British army had rifle regiments. Davy, being a rifleman would never mistake a musket for a rifle.
Factual error: Travis never took his orders from Houston, and Bowie never took his orders from Travis. Colonel Neill (not Houston) left Travis in charge at San Antonio while he went on a 20-day furlough to be with his family - not to go north with Houston (since Houston wasn't there to begin with). Travis then rashly asked the militia to elect a leader, and they chose Bowie. Eventually the two agreed to share command, Travis over the regulars and the volunteer cavalry, Bowie over the garrison volunteers. By February 24th, however, Bowie was very ill (probably with typhoid) and was bedridden for the rest of the siege, leaving Travis as the de facto commander. In the movie, he isn't confined to his bed until the final assault, and then as the result of a wound.
Continuity mistake: When Crockett's party first see San Antonio, they are carrying little more than blanket rolls on their horses - and no pack mules. However, when Crockett tells them to change into their best duds, top hats and other clothes appear from nowhere.
Factual error: The final assault began before dawn, around 5:00 in the morning. Travis was killed almost immediately by a shot in the head.
Factual error: The facade of the chapel is slightly anachronistic: the two upper windows were not added until the 1840's, and the top was more level - for the movie, it was deliberately distorted to suggest the famous hump by which people recognize the Alamo today. The chapel itself was built to scale, but the rest of the compound is about 75% as big as the original - otherwise, the Alamo compound is generally quite accurate.
Factual error: Sam Houston twice places San Antonio on the Rio Grande (once he calls it the "Rio Bravo," which is the Mexican name for the same river). But San Antonio is on the San Antonio River, about 150 miles from the Rio Grande. Travis likewise seems to have a shaky grasp of geography. When he is explaining the situation to Crockett, he makes an "X" in the dirt and says that that's Santa Anna. Then he makes a line to represent the Sabine River. On the opposite side of the line, he makes another "X," to represent Houston. Then he jabs his sword into the dirt and says, "Somewhere in between . . . is the Alamo." His little map puts both Houston and the Alamo somewhere in Louisiana.
Factual error: Houston sent Bowie to San Antonio with orders to blow up the Alamo and withdraw to Gonzales. It was Bowie's idea (not Travis's) to stay and fortify the Alamo.
Visible crew/equipment: During the battle scene, you can see stuntmen falling on mattresses. Just after Crockett tells his men to take Bowie into the chapel, someone actually falls off of a wall and bounces.
Plot hole: When Travis makes his speech offering the men a chance to leave the Alamo, and opens the Alamo's gates, Bowie and Crockett are about to leave with their men. Yet it is broad daylight and the fort is already surrounded. Where is anyone going to go?
Factual error: Colonel Fannin's men were massacred after the siege of the Alamo, not before. The most likely reason Fannin never got to the Alamo with reinforcements was simply that he didn't have any supply wagons
Factual error: Travis calls Susannah Dickinson his "cousin." They were not related. And Susannah would have been about 15 years old, with black hair, while her daughter, Angelina, was about 15 months.