Jack Reacher's creator does state that Reacher has a photographic memory
He also has a photographic memory and a keen eye for details that
ordinary investigators overlook.
I've watched the scene with Jack and Sandy twice and I can't pickup any reason why he asked her to write it down. He barely looks at it and we don't get to see it. He doesn't do anything with the paper later on either.
I did notice that she continues to talk while she writes it down though. This may have been to not bore the audience with her rambling off an address that would be unimportant to the viewers. It was also a more natural scene (as you and I would have played it out). The scene with the quarry address seemed more like posturing than to show off his great memory. He was trying to intimidate the other guy after all.
Unfortunately I've looked a great deal and there just doesn't seem to be any specific reason so I can only offer speculation that he may have intended to give the paper to someone else (possibly a deleted scene?).
Edit: I've been reading the book and in the book, reacher doesn't get the address from Sandy, he gets it from Gary. He forces Gary to pull Jeb's employment file and get the address from it which would require Gary to write it down.
The scene with Sandy was quite a bit different in the movie than the book, so it looks like they combined the two interactions from the book into a single one with Sandy.