But - - I didn't write what I do.

How interesting that LT Homepage headline says: 'Library thing connects you to people who read what you do.'

I don't think so!

Do they mean: 'Library thing connects you to people who read what you read'?

To me there's no ambiguity in the LT phrasing--it's not parallel to 'he sees what you do' which could mean either 'he sees what you're doing' or 'he sees the same thing you do'. To me, it would need 'about'--'Library Thing connects you to people who read about what you do'--to mean that I'm in a sort of low-tech Truman Show.

It reflects the use of "do" as auxiliary, a replacement verb.

"Do you read? I do (read)."

"You read. I do (read)."

Not an error, although possibly more colloquial than formal.