"In the old days", I think there was much more emphasis on, and valuing of, scholarship, in the sense that there were (usually older...) people who had good memories, and had paid attention, and knew of many things. Published and preprint-only. I myself was struck by this possibility most powerfully as a grad student at Princeton long before computer look-up was possible: many of the math faculty were aware of an amazing terrain of current and older work.
In some regards, this was very important there, because very many of the most important books and journal volumes were checked out, all the time... and grad students had very low "recall" priority. So to be able to find out what was in those unavailable sources, informally, very quickly, by talking to scholars, was excellent.
Unsurprisingly, the high-level "pre-processing" done by very-capable scholars, as opposed to search engines, allowed many huge speed-ups in searches... and I think still does so.
And, with live scholars, as opposed to current fairly-generic search engines, one of the fundamental difficulties... not knowing the keywords... was easily overcome.
Indeed, from what I can see, quite a lot of the "research" posted on arXiv has failed to connect with much prior research, visibly due to failing to connect to the proper key-word (or author) world. Understandable, but "computers" do not magically solve that problem.
One of the biggest changes is simply the possibility of typing things up oneself, in presentable form, and easy error-correction. This was a significant bottle-neck as late as the late 1980s. The even bigger change, unimaginable in 1985, was the possibility of "publishing" by simply putting things on-line. "Organizing" this, if we pretend that's what we're doing, to any degree, seems to require new ideas or concepts, that are not yet "here". E.g., for math, arXiv is very useful, but: lots of pointless stuff, and many things don't appear there. (I periodically check the web pages of a list of people to see what they're doing... in addition to looking at arXiv daily.)
But, yes, "in the old days", it was important to "be on the inside", and/or be connected to people who were, etc., to get the "preprints" which would not have been (could not have been) publicly available for a year or two (due to publication lag in math... which sometimes was infinite).
And, as other answers have noted, in those days, in math, conferences really were the places where new things were announced... that might not appear in "publications" for a year or two, if even that!
We can also mention the vagaries of "physical mail", especially transatlantic... :) Things could take a month or so, or never show up at all. And, too, long-distance phone calls in the U.S. were pretty expensive. People tried to arrange to charge their grants... :)
One summary of the state of things was that there may have been a more coherent common body of "known" things, that specialists/experts all were aware of... and novices were trained-into that scholarship.