As a wood floor professional myself, I always tell my customers it never matters what I think, they're the ones that have to live on it / see it everyday, so if they're not happy with something, we're going to fix it. We are held to a different standard than most in my town, and we deal with some of the most "particular" customers known to man.
With that said, I'm in no way condoning this job, or dismissing any complaints about it, but I would like to point out to everyone else other than the OP, that these pics appear to be pretty close up. One can not even see the top of the base boards (as opposed to Flipper4pups pic). Taking pics this close doesn't always give a fair representation of problem areas. If one was looking at something like this from a standing position, it would look different than a pic taken 6-12" away.
For reference, standard base shoe (which is what this appears to be) is ½x¾". Quarter round would be ¾x¾". With the shoe being ½" thick, those gaps aren't as large as one would first imagine just glancing at the pics. Again, I am not defending the job in question at all. Just saying that close up pics like this make these kinds of issues appear a lot worse than they would in person. For the floors themselves, the National Wood Flooring Association (yes, it's a thing), basically has a standard on things not sticking out from an upright position. In my opinion, the base shoe installation is sloppy, but the pics definitely exaggerate it. And I could be mistaken if seen in person. All we have to go by is these pics.
If you need to touch your toes or drop to your knees with your nose on the floor like a bloodhound, you're grasping for straws (in general, not necessarily this situation). Always love my customers that would crawl a wood floor with pieces of tape everywhere trying to telling me things like knot holes(closed, not open) in the wood (some smaller than an eraser tip) are my imperfections and need to be fixed. No matter what though, we always go above and beyond to make them happy, even if that means educating them about characteristics of wood.
Outside of the trim, how does the rest of their job look ? Are you satisfied with the floors themselves, or are there issues with that as well ? If trim is the only concern, then that should be the only part of the bill to be contested. Am curious, was this installed by a big box type flooring store, or a local mom and pop shop ?