The ship has a Navigational Draft of 31 ft. The US Army Corp of Engineers maintains a 9 ft navigation channel above Baton Rouge, LA to Cario, IL. Therefore, the ship could not travel up the Mississippi River.
It is stated that the ship is out of weapons because the magazine room had to be flooded in order to put out a fire. This would only temporarily make them unable to reload the ship's missile and torpedo launchers, they act as if everything in the magazine room was ruined when it got flooded. However everything in there is designed to be waterproof, as soon as the water was vented from the compartment they would have access to all of their weapons again.
In the DVD extras, "Sic Semper Tyrannis" is said to mean "Death to tyrants." It is more closely translated as "Thus always to tyrants."
The over flight of St. Louis looking at the Arch is outdated by at least 3 years. It does not show Ballpark Village; instead it shows a construction site. It also does not show the construction of the City River Arch project currently ongoing - though, that edit is completely understandable.
The president mentions the "College of Memphis" in Tennessee. The proper name is the "University of Memphis.
When Tex spreads the contagious cure to the rancher at the farm where his daughter was staying, and then again to the sick man who was shot, he failed to tell them that he had not only cured them but had also made it possible for them to spread the cure to other people. That would be critical information that they would need to know, not only so that they didn't have to worry about getting sick anymore but also so that they could know how to spread the cure to any other people that might know or meet.