These days vidga passwords aren't a issue since either:
1)Games don't use these anymore since the mid 90s
2)If you're playing digital copy of a game it will have a save system added in or at least a suspend state
3)Using a emulator and just use save states be it willy nilly or more appropriately at the password screens.
Even then if you refuse to use save states, playing with the original cart or a flash cart, you don't have to write it down but can just take a picture of it with your smart phone. Still a pain in the ass to put in but you don't have to write every character down and possibly make a typo by accident, ruining your password.
But what about back in the day before emulators and phone cameras were common place? How could you quickly record your password? Taking picture with a normal film camera disposable or not would be both wasteful and inconvenient since you need to develop the whole roll to see the password. I suppose you could use a Polaroid camera to take screenshot of the password, but this has a possibility of not having enough clarity to see the password at worst, and at best would be costly in the long run.
But what about VCR tapes? Now not everyone had a VCR camera but they did have a VCR that could record tv shows and what not. It's very possible that you could just set your VCR to record your gameplay, I mean AVGN did as a kid when playing mega man. That way you could just jot timestamp of the password on the sleeve of the tape. Then when you wanted to continue the game you'd just load up the time to the proper time, pause it, alternate between the game and the recording until you finish typing the password.
Now I'm not saying that people did do this, but rather this would be a more reliable method of password storage than just jotting it down. Did anyone do something like this with password save games?