Next of Shin - S3-E5
Continuity mistake: As Hank is having his discussion with Cotton in the Casino you can see Cotton's red (playing) chips in front of him. In one shot Hank stands up and the angle shows Cotton from over Hank's shoulder and the red chips look black and badly damaged. The next shot from the same angle the chips are back to being red and completely fine. (00:19:55)
Next of Shin - S3-E5
Continuity mistake: During the scene where Hank is talking to Bobby in the garage about the baby, Hank is wearing brown shorts and sitting on a stool. When Hank stands up you can see the top of his pants are now blue, the same color as his usual pants. When Bobby passes in front of him, he has brown shorts on again. (00:11:00)
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.