In the I Love Lucy Christmas Special where the gang are reminiscing about old times, at one point Fred turns on the lights on the tree and within 10 seconds, they pop back off. Pay attention to Lucy during this scene, she deliberately pulls the plug on the tree, causing the lights to pop off. She covers up for it by laughing.
In "Redecorating the Mertzes Apartment" #74, after the feather fiasco when Lucy and Ethel are in the Ricardo's living room, you can see a feather float down from above the set!
In "Too Many Crooks" #75, when the girls tell Fred which way the REAL Madame X went, Fred runs the opposite way, which would take him right out to Lucy's living room window!
Lucy says that she can only play "Glowworm" on her sax in "The Saxophone" #40, but later on she says she can play "Sweet Sue" and knows several other tunes when the dreaded instrument comes out.
And what happened to Butch, Fred's dog in "The Diet" #4. We never heard of him again. Plus, when Little Ricky brings "Fred" the dog home "Little Ricky Gets a Dog" #165, we find out that everyone signed a lease saying no pets... AND in #9, "Drafted", Lucy believes she hears Little Ricky crying, but Ethel explains that it's just Mrs. Trumbell's cat. Mrs. Trumbell also asked Lucy to buy her a can of All-Pet for her cat in "The Business Manager" #100. Hmmm... guess it was landlord privilege.
In "Lucy thinks Ricky is trying to Murder Her" #1, the couch in the living room is different from the couch in "The Girls Want to Go to a Nightclub" #2. It was the same style... almost.
When the cast gets ready to go to Hollywood, they state that they'd never had a car before. But when Lucy and Ricky go to Connecticut to "renew" their vows ("The Marriage License" #26), Ricky is driving a car (since he owes the gas station man money and since he says several times I'll go get the car). Now this could simply be because the car was rented for something but I found it rather interesting.