If the back of a 1975 dime is smooth at least a 1-4 inch from the edge but the very center is normal is this a mint error?

It sounds like an error in the coin stamping process. When coins are minted, a round, blank piece of metal is punched out of a strip of flat metal. The flat planchet (the minting term for a blank coin) is then moved along until it is between two steel dies that have the coin's reverse images engraved on it, one side of the die is pressed downward onto the planchet as it rests on the opposite die. Sometimes these dies will come unbolted and rotate or become misaligned and produce a coin with a crooked or off-center image. Coin collectors love these "error" or mint fault coins. It is certainly worth something to the right coin collector. I would put it on eBay and see what happens.