Bug Quake? Lifts doesn't work, etc

I have been playing Quake and have been encountering several bugs that are forcing me to use cheats to perform what should be accomplished through "normal" game actions.

For instance, on the Necropolis level, there is a small area under a bridge where there is some zombies and a small secret area with rockets on it. I jump on it, perform what I want to do. To go back, there should be a lift on its left side, but when I go to there, there is only the mechanism, but no lift.

Latter on the level, there is a similar issue with another lift

On the following level, Grisly Grotto, there is a big lift that takes someone to an upper level, where there is a trap that shoots nails. However, when I jump on it, it goes up and I just go through it, as if I was a Phantom! And on the upper floor, if I step in all wood squares on the floor, that triggers the nail traps, it should open openings on the floor, where I would be able to access on the lower floor where there are buttons to push, necessary to enter the Zigurat secret level.

However, when I step in the wood squares, nothing happens!

Anyone experienced such bugs? If so, how can I fix them?