In episode #124 "Harpo Marx," Lucy had a friend named Caroline Applebee, but in a later episode #47 "Club Election", Lucy bribed the same friend only now her name was Lillian Applebee. To find out the reason her name was changed, visit the "I Love Lucy" Facts page.
Ethel Mertz's middle name was Louise in "Lucy and Ethel Buy the Same Dress" #69, but in "The Middle-Dollar Idea" #79, it had become Vivian's real middle name, Roberta. In "Ethel's Hometown" #113, it was Mae.
Episode #54 "Ricky Has Labor Pains," Lucy is sitting in a big comfy chair reading a magazine which if you look closely you can see she is reading an article about the show she's in. The front cover clearly says: "I Love Lucy". (Thanks to Nick at Nite Rewind)
#44 "Ricky Loses His Voice", when Ricky is singing in the beginning of the show with Marco playing the piano, he tells Marco to call Lucy. Marco answers with, "OK, Des."... instead of Ricky.
#43, "Redecorating"; you can see Fred waiting in the hallway to come on for his scene. It is when Ricky wants to check out what Ethel and Lucy have done where you see Fred behind them in the hallway.
In "Vacation From Marriage" #41, Lucy and Ethel are in the kitchen talking about how each of them can predict what their husband will do and say down to the last word. Ethel says "he hasn't varied 5 minutes in 22 years." Then in the following scene, Fred says that after 25 yrs of marriage Guess to Fred it feels like 25. :-) But then again in "The Courtroom" #42, they indicate it's for the 25th, yet only one year earlier the had celebrated their 18th anniversary.