Update:
- Fixed the back corners of the bottom floor.

Update:
- Very small changes aiming at reducing calculations when they are not necessary. Should lower the potential for lag a little bit.

Wrong update. :)

Update:
- Added an experimental feature - gradual acceleration and slowing down;
- Added VCZ Elevator Experimental (the only block that has the new feature for now);
- Small code optimizations;
- Sealed the floors from all sides except where the door is. This will allow you to pressurize the elevator shafts without worrying about lag when opening and closing the floor doors.
- Changed the floor doors sound to a less annoying one.

Update:
- Fixed the check for elevator cabin going above the top floor.
Now if it can't stop at the top floor it should start going down again.

Update:
I did some tests again, this time on my laptop. The poor thing was barely running with 10 FPS and 0.30-0.40 sim speed. I was having all your issues with falling trough the floor and cabin going past the top floor.
Falling trough the floor was mostly caused by a lag spike at the start of the elevator moving. I have made some adjustments to compensate for that. Also I increased a little bit the margin of error for stopping when reaching the floor. This helped a lot but it may also cause some small misalignment of the buttons. Please pay attention to which one has lit up in yellow.
Of course in these extreme conditions of the game even that didn't help much so I added a new block called "VCZ Elevator 5m/s". As the name implies it has reduced speed to 5 meters per second. Use that in case you still have problems.
I also added a very lazy check if the cabin is running wild. If it does go out of the elevator it should automatically come back. I know it's not much but at least it might spare you some running around figuring out how to get it back (or grinding down and rebuilding the main elevator block).

Please let me know if any of this has helped.

@ posthy, I will need to see your world to find out what is happening.

Irrelevant small update.

First upload.