Peggy Hill: the Decline and Fall (2) - S4-E1
Continuity mistake: Hank discovers Peggy lying on her back in the field. In the previous shot Peggy fell face first towards the ground. There wasn't enough time for her to turn around before hitting the ground.
Peggy Hill: the Decline and Fall (2) - S4-E1
Continuity mistake: In one scene Hank is helping Peggy scratch one of her arms that is in a cast with some normal straws joined together. At first he is holding the last and first straws and there is only a few straws. The next shot he is holding the straws with one hand about halfway down (2-3 straws down) and there are more straws then there was before. After this shot the straws revert back to how it looked originally.
Peggy Hill: the Decline and Fall (2) - S4-E1
Continuity mistake: Before Hank starts arguing with Cotton near the end of the episode, Cotton has a can of beer in his hand. When Cotton is being held by Hank and swinging his arms at Hank the can of beer has disappeared. There was no moment where we can hear him drop the can, and as he pushes Hank we never see him drop it.
Peggy Hill: the Decline and Fall (2) - S4-E1
Continuity mistake: When Peggy is drinking the formula for breakfast, she has a small napkin placed over her neck cast. As Peggy and the baby start crying the napkin has disappeared.
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.