Say I have a small problem which can be solved easily by myself. Yet I don't do it because of some unimportant thing, and this involves many people and generates many debates, making everyone fed up. Is there an idiom or common phrase for this?
You could describe is a "'for the want of a nail' situation".
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
It doesn't give the sense of a personal fault that leads to it, but I can't think of an idiom that says that, possibly because we don't generally like to criticise ourselves that much!
You seem to want an idiom where the effect is felt by others, rather than just by you, so one of the phrases we use to stress the value of early action might be a good choice.
A stitch in time saves nine
comes to mind. The idea is that when something starts to go wrong immediate action is better than delay.