In "Sales Resistance" #45 Fred buys Ethel an new Handy Dandy washing machine. However, a mere 14 episodes later in "Never Do Business with Friends" #67, Ethel calls her washing machine an "old relic" and says, "honestly, I think it was one of the first ones ever made."
In "Paris at Last" #145 Ethel says she bought a bag when she went shopping. It was a leopard print document case. Earlier in "The Passports" #138, when Lucy goes to visit Helen Kaiser, Lucy is carrying that very same bag.
In episode #65 "Ricky's Life Story", Ethel is looking at a picture of Ricky making arroz con pollo in Life magazine and says that she' seen him like that a dozen times, but in episode #39 "Job Switching", Ricky definitely CANNOT make it.
There are quite a few episodes where Ricky mentions that he couldn't speak English until he came to the USA, but in the Lucy-Desi Comedy Hour episode #1 "Lucy Takes a Cruise to Havana" Ricky CAN speak English.
In episode #36 "The Anniversary Present", Ricky gives Lucy a string of pearls for their anniversary, but in the Lucy-Desi Comedy Hour episode #12 "The Ricardo's go to Japan", Lucy doesn't have any real pearls and is determined to get some.
In episode #30 "Lucy Does a TV Commercial", Take a look at the curtain that hangs down the back of the TV set. After Lucy gets out the curtain is on TOP of the TV and Desi promptly pushes it down. In the next cut to the master (obviously a different master) the curtain is back up again. (thanks to email@example.com)
In the episodes where they celebrate their anniversaries, the date changes from episode to episode. In episode #121 "Hollywood Anniversary" they say it is on one day and in episode #36 "Anniversary Present" Lucy makes a big deal about a day circled on the calendar, but it is a different day! (thanks to firstname.lastname@example.org)
Episode #88, "Ricky's Hawaiian Vacation", when Freddy Fillmore asked Ethel & Fred whose mother she was, they said it was Ethel's mom. Ethel's last name was Potter. When Freddy told everyone that Mother Mertz was sick, it should have been Mother Potter.