The wrong university might result in someone in the hiring committee smiling for a second. It is a copy and paste error, which would only become a problem if applying to University A would be an error in itself, e.g. if A is the school of astrology in Hoople, Southern North Dacota, and B is the MIT. 

The wrong date will not be noticed by anybody. If you have to look at 60 applications, you do not read every letter line by line, but just skim over it to see whether it contains some real information, like "was very engaged in teaching/student union/environmental issues/...". 

A large part of the meaning of a letter of reference is independent of the content of the letter. If I believe that X is good and honest, and X writes a letter for Y, then I guess that Y cannot be too bad.