Should my new open cell insulation look this messy and uneven?

That's a completley unacceptable install. While open cell foam expands rapidly and doesn't always look like a smooth sheet, seeing the subfloor means you have zero **air seal** in those spots. The whole point of using spray foam for a garage ceiling is to stop drafts and thermal transfer to the bedroom above. If you can see wood, the contractor failed at the most basic part of the job.

I've sprayed quite a bit of this stuff, and while it can look like a mess of popcorn, it has to be continuous. Those gaps are basicly chimneys for cold air in the winter and humid air in the summer. It's not just about the thickness; it's about the fact that it isn't bonded to the substrate everywhere. If they missed spots in the middle of the bays, they probably missed the rim joists and headers too, which is where the biggest leaks usually happen.

You need to get that rig back out there. Don't let them tell you they'll just send a guy with a few cans of retail foam or a small froth pack to patch it. A professional crew should be filling those cavities until they are consistently covered to the depth specified in your contract. If you're planning on putting up drywall later, they should be trimming the excess back flush with the joists anyway, which would reveal those voids immediatly. Grab a can of bright marking paint and circle every single spot where you see the subfloor. Check the corners and where the joists meet the exterior walls especially closely. Make them respray those areas until there's a solid, monolithic layer. If they're a reputable outfit, they'll know this is a sloppy job and fix it. If they push back, they're just hoping you won't notice the lack of performance once the seasons change.

I was looking into getting this done for my bonus room, but seeing this makes me second guess the contractor I called. If there are gaps like that, does it mess with the soundproofing too? One of my main goals was to quiet down the garage door opener noise from vibrating thru the floor.

Also, does the foam need a special coating if I'm leaving it exposed in the garage for a while? I heard some stuff about fire safety but I'm not sure if that's just for certain types of foam or if it's a code thing.

One thing people overlook with open cell in a garage is the fire code. Since it's an occupied space above, you ussually need an ignition barrier or 5/8" fire-rated drywall over that foam. If they left it exposed and messy, they probably didn't mention the R-value drop-off. Open cell is only about R-3.5 per inch, so if they skimped on depth in those thin spots, you're barely getting any protection. Plus, open cell isn't a vapor barrier, so you might get condensation against that subfloor if the garage stays damp. Definitely make them fix the voids before you even think about closing it up.

Check if any of that foam feels 'crunchy' or stays tacky when you touch it. If they were rushing and didn't have thier temps or mix ratio dialed in, you might have a bigger problem than just gaps. Badly mixed foam can off-gas a funky smell for ages. Also, since open cell is vapor permeable, those thin spots are basially letting moisture move right up to your subfloor. If you live somewhere humid, that can lead to mold issues under your bedroom floor. Definitely don't pay the final bill until every bit of wood is covered and it's cured solid.

The contractor was definatly trying to stretch thier yield on your dime. When they move the wand too fast across the bays, you get those 'holidays' where the foam doesn't have time to properly knit togather. Since you’re seeing wood, you’re basically getting zero R-value in those voids because the air just circulates right past the foam. Take a thin wire probe or a meat thermometer and check the depth in those 'thick' spots too. Sometimes they over-expand the mix to make it look full, but it’s too airy and won't meet the density specs. If the coverage is that spotty, they likely skipped the rim joists entirely.