In the Pilot of the series, CD says he was a ranger 5 years. But in season 2, Alex asks him how long he was a ranger for and he says "28 years" In the episode where CD was inducted into the Ranger Hall of Fame, it was announced that CD had 30 years of service.
Walker's black hat does not conform to law. Uniform regulations for Texas Rangers require a "light-colored and shaped in a businessman's style" hat (per Texas reg. Section 06.25.01). Black and brown are not authorized. Incidentally, though, the hat does NOT have to be a "cowboy" hat, but "Styles commonly called the Rancher or Cattleman are recommended."
Alex Cahill bears the title of "Assistant/Deputy District Attorney," which implies that she answers to a head DA. Yet no such person is ever seen, mentioned, or heard from throughout the series. Moreover - despite effortlessly convicting every criminal she prosecutes, and despite instinctively knowing whether or not a suspect is guilty - Alex never receives a single promotion in ten years.