I’m thinking they could definitely be used to mount the cortex, batteries, LCD screen. Where else?
You could possibly use it to hold bearing flats. But at the point you might was well use pop rivets.
The build coach does not allow pop rivets (except in very special circumstances)! So nylon screws and bolts would be perfect for bearing flats. That would save a ton of weight!
I wouldn’t use them for the battery, actually. The screws are restraining a lot of weight there.
Things like bearing flats, sensor mounts (depending on the sensor), number panels, etc. are other possible places for nylon screws.
I really hope you don’t need the weight that badly, though.
Nylon screws seems to have the connotation of being very flimsy, and to be honest I too sometimes think to myself how they could even be useful. 
Beyond light duty tasks like holding a battery or number plates, there’s many other uses such bearings and structure. You might need to use a few more nylon screws than steel screws to be safe, but 2 normal screws with nylocks weighs about the same as 15 nylon ones, which can still be a significant weight saving.
The main areas I would not recommend nylon screws for are things that are under high stress such as the mounting of an arm, or screws that would experience strong rotational forces because you can’t get nylon screws as tight as steel. It does definitely take getting used to using them, but once you figure out what works best where it can work very well.
No, not nylock, we’re talking about nylon. That means the screws and nuts are made out of plastic. The same kind of plastic the white spacers are made of. These are non-vex parts but are legal if the right size and commercially available. Easy mistake, though.
Oh sorry I kind of misread it.
I use nylons on linkages, bearings, and structural connections among other things. they are great in any place where the load isn’t high enough to snap them. They might bend but that is usually fine. I don’t have to use nylocks on them either, I’ve never had an issue with a nylon screw coming loose from a nylon nut. so basically anywhere that is getting < 15 lbs of force.
Eventually, I’ll get some and have our students test them using vex-metal fixtures in the materials lab here at MCCC. Then we can all have some hard data on nylon vs. steel, rather than just assumptions and gut feelings.
Depending on the linkage, a nylon screw as a linkage pivot is definitely not a “safe” application for them, and somewhere I would be extremely cautious. Don’t go overboard trying to save a couple of ounces.