FTDK
That trick has worked for me too, whether I've entered the wrong code or departed with a code from a previous flight. So if Centre or Approach make an error do we write them up too? I've had my Call Sign transposed by them more often that I've screwed up with the transponder.
I find myself getting read-backs screwed up now and then, but then that's why they have it - so you don't get it wrong. I write clearances down and then only read back when I've got it all down, even if it means a "pause" while I finish writing before I read-back.
I make a habit of trawling through the ATSB Weekly summaries (that get updated monthly) and there are plenty of "errors" by RPT in non-compliance with SIDS and STARS, or not updating waypoint ETA's, and they have TWO crew up front.