While Lucy is somewhat consistent in her lack of talent, Ethel at various times is shown to be excellent on the piano, as well as, having a very basic playing ability. In one episode, she plays 'Sweet Sue' and other songs while the group sings, but in various episodes where Lucy is trying to form a band, she is hopelessly inept on the instrument.
When the Ricardos are moving to the country, Lucy is standing for the last time in the apartment and talks about how she will miss the place since they lived in that apartment for 15 years. However they had only lived there for 4 years. Prior to that they were in the other apartment in the same building.
Lucy and Ricky swap apartments with a couple downstairs; therefore, in most episodes they are in 3D (and thus on the same floor as the Mertzes), but in some they are in 4A and living upstairs from the Mertzes.
The Ricardos are said to live in an apartment at 623 East 68th Street, which in real life would be located in the East River. This is not actually a 'goof' because it was done deliberately to avoid legal issues with an actual address.