How do I know if olives have gone bad?

They are sitting in brine. They may be saltier, but I doubt if there are any pathogens.

They stick guns in your face when you open the jar?

And generally the brine does keep them edible for quite a while. However, if you see something growing on the surface I would think it is time to get rid of them.

Thanks for the advice. I used them – they tasted fine and I cooked them anyway.

They’ve gone bad when they start forming gangs and you open your fridge to find graffiti on other jars.

R U shitting me?

Usually, they eventually discolor (a rather odd gray shade that looks unhealthy), but they keep fairly well.