There were "slipstick contests" where the "fastest guns in the West" faced off with their slide rules to compute various equations. It was even a team sport at some colleges, apparently. I have yet to see any actual photographs of a slide rule team.
It seems that many of the techniques that were used to rapidly arrive at an "answer" have been largely forgotten. One of my favorite slide rule tricks I discovered playing around with them was one I later discovered was also used by the celebrated physicist Richard Feynman at Caltech during his lectures.
Feynman (as many of you probably know) was quite skilled at mental math without need of a pencil or calculator for many of the problems he demonstrated on the board. He could occasionally produce a correct answer, using his simplex Pickett rule, to include four or five figure answers. For multiplication of two given numbers, for example, he would mentally multiply the last digit of each number together, then pretend to find this final digit on the rule itself. He never admitted using the technique, exactly, but it's largely believed by the faculty that that's how he was doing it. Probably "old hat" to some of you who actually had to use a slide rule in school.
Anyway, speaking of techniques, I never bothered to learn how to use the CI scale at all until I read an English translation of one of the Japanese Hemmi manuals and it was quite a revelation. There are a lot of different ways to skin a cat using a slide rule, I guess is what I mean by this rambling post.