Should a recommendation letter for graduate school contain the writer's contact information?
Yes, probably. In general when you communicate with someone it is good practice to make it easy for them to get in touch with you again.
Many recommendation letters (admittedly mostly at the higher levels) end with "Please contact me if you want further information." And while doing graduate admissions in my department I have (occasionally) contacted a recommender for further information.
It is hard to see the downside of this. The people who read these letters are conscientious, busy professionals: they're not going to start spamming you or calling you up for frivolous reasons. The lack of including contact information might possibly be perceived negatively, but we well know that such letters are written quickly by busy people, so it is more likely to be perceived as an oversight. Furthermore, increasingly many academics have a website which tells how to reach them, so if I can google the professor's name and find out their email address that way, no problem. I would still feel free to contact them if I had a question to ask.