If the NPCs are using objects that the main character can also interact with, will that cause a glitch problem? What happens when you go inside an apothecary store and knock down all the potions the NPC was working with? Will the movement of those objects confuse the computer and cause serious glitching? Will the NPCs be intelligent enough to find where you've moved the object and pick it back up? Will the objects automatically respawn into the appropriate place when the NPC needs to use them? Or will they make certain job related objects non-interactable for the actual player?
The only thing that makes sense to me is that certain objects would respawn when the NPC needs them, because what if you decide to steal an object the NPCs use? It would look ridiculous if an apothecary just kept waving his hands around as if he was creating a potion, but without any sort of bottles and ingredients.

I don't have much programming experience, so maybe there is a much more simple way of solving this problem. Do any of you have ideas on how this problem could be fixed?

Hm... I don't really know but i think that would be the case if the NPC interactions were just scripted movements. I don't think that is the case, I think they are tasks that the NPC AI knows it must complete. It will simply use items if they are there, if not then theoretically the NPC will seek out what is required before completing the tasks. ie, fetch another broom or purchase some potions or whatever.

^ this. bethesda knows whats up when it comes to this stuff, theyve had problems with AI in the past but i honestly think Skyrim will break the "norm" of AI defficiency.

Radiant AI is meant to make NPCs fetch the items they need for tasks themselves. One extreme example from the development of Oblivion is an NPC killing another NPC to get a broom so that they could do some sweeping. That is actually one of the main features of Radiant AI, NPC reacting to items in their surroundings and using them to complete tasks. There have also been mods for Oblivion that made shopkeepers move goods back onto the shelves if you moved them.