en.wikipedia.org/wiki/Battle_of_the_Alamo

This date is off by at least a year.

Official Alamo materials say an 1849 drawing by Captain Seth Eastman shows the church before the Army’s roof-and-facade alterations were completed. The Alamo’s own U.S. Army Quartermaster history then states that in 1850 the Army’s Quartermaster General ordered the roofless church repaired and a second floor created. The Alamo’s educational materials also note that the parapet/arched cap was added in 1850 by the U.S. Army.

So the Army did alter the church, but the year given here—1849—does not match the Alamo’s official chronology, which places the roof/parapet work in 1850.

This sentence reverses the publication chronology.

The Alamo’s own historical overview says that "Not until 1860" was the public presented a detailed analysis of the battle, referring to Reuben M. Potter’s The Fall of the Alamo. By contrast, John Henry Brown’s major Texas histories were published much later: Google Books lists History of Texas; from 1685 to 1892, Volume 1 as published in 1892, with the second volume appearing in 1893.

That means Brown was not the first person to write and publish English-language histories of the battle. Potter’s Alamo history appeared decades earlier.

This sentence misstates what the $400 million figure referred to.

Contemporary reporting on the Moses Rose’s dispute consistently describes a $400 million Alamo redevelopment / expansion plan, not a $400 million property. The Reason article this passage appears to draw from says the owner’s refusal allegedly put the entire $400 million Alamo expansion in jeopardy. KSAT likewise reported that the bar site sat within the footprint of a planned visitor center and museum that was a central part of the $400 million plan.

In the same KSAT report, the bar property itself was appraised at about $2.1 million, with the city’s final offer at $5.26 million—further confirming that "$400 million property" is incorrect. The $400 million figure was for the overall project, not the individual parcel.

This caption confuses the subject of the 1936 stamp.

The Smithsonian National Postal Museum says the March 2, 1936 Texas Centennial stamp did not commemorate the centennial of statehood but instead commemorated the centennial of adoption of the Texas Declaration of Independence. The same museum page says the stamp features Sam Houston, Stephen F. Austin, and an image of the Alamo.

A separate National Postal Museum page notes that the Alamo-specific 9-cent stamp was issued later, on June 14, 1956. So the 1936 issue was not a centennial stamp for the Battle of the Alamo itself.