Earlier today, and in other occasions, I've experienced a strange phenomenon. It seems the desync or lag on the servers is client-side, or at least it looks like that. After about 10 or so minutes, zombies, players and doors start lagging, as well as picking up stuff. If you reconnect, everything's normal again. It feels like there's something overloading the client connection or "thinning" it out, and rejoining clears that blockage out.
The problem with doors, which I've noticed, is that the object itself (the door prop) swings and opens/closes fine, but the hitbox itself of the door, that one that stops you from walking, is very desync, opening very slowly. Sometimes it is in sync with the prop, and it can be noticed how both open in "frames" so-to-say.