Now that I live in the opera world, pretty much all my shows are 100+ people.
I have the chorus and supers wear nametags, color-coded by voice type, throughout staging rehearsals.
I notate blocking using initials (make a quick check before rehearsals begin to identify any repeat initials, like Brad Smith and Betsy Sledd). Prinicipals are notated with the character's initial inside a circle - this also helps the principals stand out on my blocking pages that end up covered with scribbled initials. Also, stage management usually makes little wallet cards for ourselves listing principals and small roles. This way we can always pretend to know their names. Eventually we'll get the chorus. Or maybe not - which is unfortunate and a little cold, but not a tragedy.
In order to get to know chorus/super names faster, I try to talk with people during breaks and before/after rehearsals. I get to know them, so then I remember that Joni Arnold is a little kooky about her cats, and George Parks loves to garden. It helps make them into real people and not just faces in the crowd. I also get to know stagehands this way. Actually, at load-in I write down the names of all the people working the show - by department - so that I can remember their name, especially over headset. Now, recognizing crew by headset voice alone, that's a little trickier. Also, I have some sort of chip misplaced in my brain and have trouble recognizing faces. Just when I've got the cast down, they go into dress, wigs, and makeup, and I can't recognize anyone! I warm people about this before first dress rehearsal, and they always tease me about it.