Continuity mistake: When Leanne first arrives, she kisses Luanne, and gets red lipstick marks on her. Later, when Leanne and Luanne are near the bathroom and Leanne says "I knew you would understand" (about Bill), she kisses Luanne, but there are no marks from her lipstick. Even if she mostly kissed Luanne's neck, at least part of some of the marks should show when Luanne turns to leave (after talking to Peggy).
Continuity mistake: Hank takes Bill's sock off and the guys discover his toe fungus. While they're talking, Hank is still holding the sock. In the next shot of Bill, his sock is back on. (00:02:45 - 00:03:15)
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.