I've updated all my mods (18 now) whenever new versions have been released. No problems so far. The only issues I've had are:
Many settlement building items not being available before I installed Settlement Keywords because my combined extra settlement items mods were exceeding the (remarkably low) limit.
JC's shirts and jeans doesn't work properly. I can have white shirt and light tan jeans, white shirt and blue jeans or black and white check shirt with blue jeans and that's it. The others either give white+tan or make the NPC invisible apart from their head, hands and feet (which looks really strange when they're wearing combat armour). I have a seamstress working in one of my settlements, so it seemed even more appropriate to be able to craft clothing and that was the only mod I could find which did just that. Endless mods to change clothing (most for half-naked women, which is a bit sad) but only that one for crafting basic clothing for settlers.
I also seem to have lost vanilla containers somehow. Can't find them in any menu. However, the vanilla containers I built are still there, so they haven't been removed.
The most useful mods I've added recently are "disable minuteman radiant quests" and "shut up Preston". Brilliant mods. I got sick of settlers telling me they were being harassed by raiders. Every time I went to Sanctuary, it happened. 15 people in full combat armour with 140+ damage guns inside a walled fortress with >500 defence being harrassed by a handful of raiders with pipe guns. Hopefully the mods will stop that. They've certainly stopped Preston and his endless stream of silly quests.
And I still haven't found a clean bath.
But anyway...as far as I know, updating mods doesn't cause problems. However, if you're not having problems now maybe you're better off not bothering. It would probably be a good idea to back up your saved games anyway, just in case.