Leveling joists for drywall installation
It's hard to say, I find myself noticing every imperfection that I'm responsible for. I don't easily notice imperfections in other people's work unless I'm looking for them. It looks like your joists are on about 24's so 1/4 inch per foot dip in the middle might not be too noticeable as long as it's level'ish above the doors. The doors offer a reference to level, very close to the ceiling so they are the primary area of focus. 

Keep in mind 1/4 inch per foot is plumbing drain slope. 

I'd definitely go with 5/8 drywall especially if you on 24's and shim where necessary. And avoid drywall seams around the areas in question. 

It boils down to who it's for. If it's your house and you can live with it, it's fine. If it's a customer you're going to have to consider what they'll think.

Try having a look at other ceilings in the house or a friend's house and see if you notice any dips and then check with the big straight bar.