As FlyingDice mentioned, ClearInvalidRegistrations is great to use. It's by all accounts completely safe to use. It isn't perfect though, and takes a long time. Personally, I think it's safer to just accept that if you've installed a mod and saved, you're stuck with it on that character.
This, to a certain degree. Don't add and remove script-heavy mods at the drop of a hat. That said, mods that just add content with few/no scripts are generally safe to remove as long as you ensure that you move your character, followers, and anything you care about out of them (if they're locations).
That said -- this is purely anecdotal, of course -- I haven't seen a single issue caused by using it, nor am I sure what you mean by "taking a long time"; if you're talking about the initial cleaning, I can't say I noticed any sort of delay in loading even the first time I ran the game with it. Given the ease with which you can remove mods, it's probably not unreasonable in the case of larger/script-heavy ones to go ahead and drop them if they're causing a negative impact on your experience, or if a better mod doing the same thing comes across your radar.
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Hoo boy. Still putting off going back through and updating my modlist now that I've got the DLCs. :|