Ok, I am messing with a script and while I was doing it I saw that the script would fail and result in a expression error.

The interesting thing was that after it failed the script would not fire again even after creating a new game with a new character many times until I restarted Morrowind completely. That didn't seem good to me at all. To me that means all kinds of things could go wrong if you are not on a cold boot of Morrowind.

Is this a known occurrence that happens if a script completely fails or does it mean that all kinds of bad things could be happening if people save in a state like this where a script has failed but they don't realize it.

I bring this up because there has been an argument in the past on whether or not you should only load a save from a fresh boot of Morrowind.

That happens every time a script fails. You can only restart the script by restarting the game.