HA. Error correcting codes? You realize that means the person thinking in bits would have to do that themselves. A 7-bit parity would be harder to do than just dialing the damn thing. Even then all it'd be able to do is tell you that you messed up. Something that actually makes corrections on the fly (Hamming). No way. I couldn't do it and I know how Hamming works. I really doubt a consumer could do it or would want to.
A credit card number already has a check digit. If you could make people memorize a few more digits than the telephone number that they'd like to call, you have your error correction.
(Of course, this is highly domain-specific and not very convenient. But it does seem possible.)
