If a mod is a work in progress: is there any risk in adding events and properties/variables to a script that's already running? I know that if a mod has scripts running that have event handlers and the mod is yanked out of a save file, it can leave behind loose event handlers that clutter the save file.

Is there any similar risk for adding events and properties/variables? Should I stop the script, upgrade the mod, and then start it again instead?

Ideally, yes it would be nice to be able to stop the script before upgrading. That is where the advantage of RegisterForSingleUpdate versus RegisterForUpdate comes in. The former allows for a more graceful quieting of orphaned mods, whereas the latter will continue polling forever.

Nonetheless, so long as you are not removing things, there really seems to be pretty low risk to adding new events/variables/properties/functions to existing scripts. I do it often and haven't observed issues.

(Others may be able to correct me here if they have better wisdom on the topic. I'm all ears.)

Fortunately, there's a http://www.creationkit.com/Save_File_Notes_(Papyrus) that should answer all your questions