Deliberate mistake: As Dale is taking photos of Bobby's ventriloquist doll you can see he is taking the photo from the upper right of where Bobby is standing in his house. However the angle of which he takes the photo from would be impossible as it's to the left of their screen doors and there is no window or see-through material from that angle.
Continuity mistake: Whilst the old man in the retirement home is about to give Bobby the ventriloquist doll, there is a shot of just Bobby. In this shot you can see the jacket and hat on the coat rock and the coat is on the top rack. When we see both of them together the coat rack has another rack above the jacket now.
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.