Deliberate mistake: Hank only discovers the tattoo on the back of his head after having his hair shaved off. There is no way, however, he wouldn't have noticed it before this. The tattoo artist had to shave hair off the back of his head before putting on the tattoo. While he might have not realised right away, the pain the following day and the fact that he would have noticed a large part of his hair missing would make it unavoidable.
Plot hole: Amazing that neither Hank's mother nor father ever saw the bandage on the back of his head, peeled it off, and would discover his tattoo.
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.