What was graduate admissions like before the electronic age?
Since just before the transition to the use of the Internet for admissions—in the 1980's and 1990's—the kinds of documents submitted haven't fundamentally changed. What was more difficult back then is that everything had to be printed out and mailed, and application forms had to be individually written or typed out. Deadlines were basically the same as they are now, if not a little later—all of my deadlines were in January or February, whereas now they may be in December. It's not easy, as one might imagine, to visit lots of schools in the US, and in engineering, students normally visited after being admitted, not before. As far as fees go, they haven't changed that much, I don't think—I remember the fees when I applied being about $50 to $75 per school.

As you can imagine, credential fraud was much easier to commit because there was no easy way to teleconference via means like Skype or Google Hangouts, so you couldn't really tell who you were speaking to on the phone. This was most obviously a problem in terms of evaluating the English skills of foreign applicants. I know of at least one department that completely blacklisted all applicants from China for a number of years because multiple applicants would have a colleague with stronger English skills "stand in" for them in the telephone interview, and then the accepted candidate showed up with far worse English skills than the person interviewed. Nowadays, with the possibility of teleconferencing, and with ID's included in the test documents for TOEFL and IELTS, it's much easier to know who you are interviewing, making such fraud much more difficult to achieve.

With respect to contacts, that of course applies—if you know someone who's written a letter of recommendation, and there's any questions, of course you'd want to contact the person by phone or email.