Factual error: After the Oklahoma City casino incident, it shows a brief scene where Pierce picks up Dr. Rice. The sign in the background says "Ada 15, Oklahoma City 90" on Highway 81. That highway in Oklahoma is, in fact, a real road but it is no where near Ada. The closest area that is 90 miles from OKC would be around Duncan, which is well over 50 miles from Ada. (01:06:20)
Factual error: Logan and Laura emerge from an urgent-care clinic in a small town, presumably somewhere in the Great Plains or eastern Rockies. Shortly after they emerge from this clinic, a Louisiana state highway sign is visible in the background. As the scene ends, the camera pulls back to show mountains in the background, indicating that they aren't in Louisiana.
Factual error: The climax of the movie is set near the US-Canadian border. However, the landscape is very arid and desert like, similar to the Southwestern US. No such landscapes exist anywhere near the border with Canada.
Factual error: When Logan and Laura are driving towards Canada, they are supposed to be somewhere in Oklahoma. However, there is a shot of a mountain range in the background. Those are the Sandia Mountains, which are in New Mexico.
Answer: X-24's healing factor is much weaker and slower than Logan's, and Dr Rice has to give him the serum to heal his injuries at the farm, so presumably he couldn't heal fast enough to survive the shot. It may also have been a different bullet type - the one in Wolverine didn't do nearly as much damage on impact. Makes sense that Wolverine would have possibly designed one to overcome any healing factor.