Continuity mistake: Episode 22, "Talking Shop": Whilst Bobby and Stacey are working on the car at the end, Bobby puts the wrench down on the car next to him. When he asks for the socket wrench, the wrench he had put down has disappeared.
Other mistake: When Boomhauer sees Katherine at the gas station, she says, "It's been twelve years." When Hank talks to Boomhauer in his garage, he mentions Boomhauer breaking up with Katherine twenty years ago.
Character mistake: Ben Stein asks a chemistry question about -273° Kelvin. The problem is, the scientific community never uses the word 'degrees' when referring to Kelvin. The correct way to say it would have been, "-273 Kelvin is also known as what?" Also Kelvin cannot be negative since 0 kelvin (approx -273° Celsius) is absolute zero.
Answer: Jeffrey Boomhauer is a Texas Ranger as can be seen in the final episode at the end when he sets his wallet down, it flips open revealing a Texas Ranger badge.