Deliberate mistake: When Dale calls Hank from John Redcorn's trailer, the wooden clock behind Hank (in the Hill's kitchen) has no markings or hands to tell what time it is. This is a mistake as it is the exact same shape and object as it was before this episode and I doubt they replaced the clock with an completely exact object as before. A side note on the mistake is that it may be considered deliberate as the clock in previous episodes is shown frequently in the background and will generally change between shots.
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.
Answer: Couple things, first only Peggy knew the truth about Hoyt (Luanne's father) being in prison and Peggy is the one who said he's on an oil rig. But, Hoyt is Peggy's brother, so she could have been trying to hide the fact her brother is in jail. Lucky (Luanne's husband) deduced Hoyt had been in prison, but seems to be the only other person to know the truth, so when Hoyt went back to prison, he kept Peggy's lie up to spare Luanne. Additionally, Luanne was there when her mother stabbed Hoyt and was arrested, so it's not like someone had to break the news to her and they couldn't hide the fact. With Hoyt, even if Peggy wasn't trying to protect her brother's reputation, she didn't want Luanne, who is a sensitive and emotional young woman, to have to deal with knowing both parents are in jail.
Bishop73