This morning I listened to a Cliff Richard compilation album titled Early Days. In his version of "(You're So Square) Baby I Don't Care," I noticed that the lyric is "You don't know any dance steps that I knew." I'm more familiar with Buddy Holly's version of the song (although he flips the parenthetical around and titles it "You're So Square (Baby I Don't Care)"), where the line is "You don't know any dance steps that I do."
Buddy Holly's version was recorded on 19 December 1957 and was released on his second album - titled Buddy Holly - in February 1958. Cliff Richard's version was released on his first album - Cliff - in April 1959. So the Buddy Holly version is older.
Because Early Days also includes Cliff Richard's versions of some Buddy Holly songs ("That'll Be the Day" and "That's My Desire") and some other songs (such as "I'll String along with You," "Little Things Mean a Lot," and his version of Gershwin's "Embraceable You" - all of which appear on his second album, Cliff Sings) venture into the orchestrated instrumentation that Buddy Holly also used (on songs such as "True Love Ways" and "Raining in My Heart"), I think it's safe to say that Cliff Richard was influenced by Buddy Holly.
It's quite possible that his changing "You don't know any dance steps that I do" to "You don't know any dance steps that I knew" is simply a mistake. They heard "knew" instead of "do" when listening to the Buddy Holly version. (Lyrical mishearings are pretty common. On the Who's version of "Good Lovin'" from The BBC Sessions, the line is "I asked a famous doctor just what I had" instead of "I asked my family doctor" as it is in the Rascals' version. Boyce and Hart's "Last Train to Clarksville" (famous by the Monkees) came out of mishearing the Beatles' "Paperback Writer," and the Zombies' "Time of the Season" came out of a mishearing of Smokey Robinson and the Miracles' "The Tracks of My Tears.") Changing the line might just be an-other example of one artist's mishearing an-other.
Regardless of whether the change was intentional or not, it does affect the song. "You don't know any dance steps that I knew" indicates that the singer/speaker has forgotten the dance steps that he used to know. And the cause of his forgetting them is likely his spending time with the girl who's so square. He hasn't been dancing, so he's forgotten the steps. This situation gives the song a greater depth, and it illustrates a greater connection between the singer/speaker and the girl, where the Buddy Holly version - staying in the present tense - could seem more like an infatuation that will soon pass.
The changing of the parentheticals also seems to suggest this. The more prominent title of Cliff Richard's version is "Baby I Don't Care," but the more prominent title of Buddy Holly's is "You're So Square." For the singer/speaker in Buddy Holly's version, the significance is still on the girl's squareness, which could interfere with the relationship.