Should I worry about a referee who recommended rejection being offended if my paper is accepted? After submitting a paper for review, I received a letter from the editors containing a negative report and informing me that their (editors') decision was to reject the paper. Although the paper was about six months with the referee, it was clear from the report that she did not read it, just had a quick look and wrote a report, full of typos, mistakes and speculations about what the referee thought was in the paper (as she didn't read it). 

I wrote a letter to the editor saying that I agree with their decision to reject the paper and would not dispute it. But I also expressed my opinion of the report, because I think it might help to increase quality of the review process. I had no intention to get the paper reconsidered, and even started to prepare a slightly revised version to submit it to another journal. However, they have responded that they would give it to another reviewer.

Now this situation is quite uncomfortable for me: I imagine how the referee will feel if the paper gets accepted and appears in this journal. On the other hand, the referee should be well aware of the (poor) quality of her work, so maybe she will not care.

The question is: should I care?
No, you should not worry.  Referees offer opinions.  The actual decision to accept or reject a paper rests with the editor.  The referee may very well be offended by the editor's decision to ignore her opinion, but that's certainly not your problem.