If we want to talk about dated technological assumptions in TOS, what gets me is Kelso's line in the second pilot about the impulse points decaying to lead. That would mean the "points" were made of uranium and the impulse drive was fission-powered, instead of fusion-powered as is now assumed.
Then there's the sound the computer made when it was "Working" -- the clunking of mechanical relays. Although I guess a hard drive makes a similar sound as the reader arm or whatever you call it moves across it.