And which muscles are neglected and therefore need independent exercise to strengthen them?
Smile muscles
Only my smile muscles get a work out when I ride. Any thing else will just be wasted energy.
If your goal is to be a strong rider, why worry about the neglected muscles? Do you need huge biceps to ride? They’re just extra weight and burn extra calories 
Google “Specificity of Training” for many in-depth articles.
Edit: What is your goal? Total body fitness? Training for a triathlon?
Your pinky finger extender muscles are likely being neglected… but since we don’t know your goal, we don’t know if it’s nonsense to mention that or not…
I have to work out my middle finger separately.
I was thinking about possible muscle imbalances. If some muscles are developed and other important ones are neglected, the imbalance created may give rise to injuries. So the neglected muscles may need to be stretched and exercised independently.
Clowns with Abs! 
My understanding is that if you only do one major activity you are likely to have muscle imbalances. If you really train hard in that one activity, the imbalances can lead to issues, but of what nature I’m not certain. So far I haven’t run into such problems that I’m aware of.
Generally unicycling works the legs (duh) but also the lower back and abs. Not so sure about my own abs (not much there) but I think the lower back gets pretty strong with unicycling.
calves
I notice that my calves do not get the same workout as the rest of my legs. I suppose you could use the balls of your feet to pedal instead of centering your foot on the pedal over your arches (which is how I tend to ride). I have seen some nasty achilles tendon injuries which have resulted from that.
Carey
I think it is an important question to bring up and not just say “go ride”.
I have found that inner quad muscles are neglected the most and can lead to imbalances since the rest of your quads get worked heavily. Leg press, and squats with your feet pointed slightly outward \ / did wonders for me.
Your abs and lower back do get worked, but for your abs it is all intrinsic muscles…you won’t get a six pack from unicycling.
I do not believe this is true, especially if you’re doing hardcore muni and/or trials. If I can self-incriminate for a moment, I will venture to say that there are many muni/trials/street riders who seem to have pretty good abs when they prance around shirtless in their videos…
I’m fairly sensitive to my (lack of) fitness level, and I definitely notice that my abs are a lot more toned and less prone to excess flab when I unicycle regularly, even if it’s just a 40-minute 36er blast a few times a week. While I never got to the point where I could justify throwing away my cheese grater, I do think it’s possible to get some really good abs with just unicycling.
You’re right…I have an 8-pack! 
Perhaps more important than what musccles to build up is which muscles to stretch.
Look up stretches for cyclists. These will help loosen muscles that get tight and in doing so will work to some extent the antagonistic muscles.
Here are a few good ones: http://www.grouptrails.com/Stretches.htm
And some other good ones:
Pah, that’s nothing!
I have a keg 
I developed unbalanced quads when training for RTL. They started pulling my kneecaps out of alignment and it was so bad that I could not even walk without pain. It took me a long time to recover from that and I was not in nearly as good of shape for the race as I would have liked as a result.
I found that spinning short cranks on a 27" uni really shortened/tightened my hamstrings. I started to run regularly to keep them stretched out. apparently this also contributed to the outer-quad/inner-quad imbalance. Next time I train for a uni race I will mix some swimming in with the riding and running. Should do the trick I think.
my english vocabulary is limited so I do not know how to qualify those muscles we call in France “love handles” 
(protruding around your hips) but unicycling sure developed those! (or is that a side-effect of beer I drink after riding?)
I also find my shoulders ache from balancing a lot with my arms, swinging them around and that! Could be working them out quite a bit too
I wonder if there is connection between beer and unicycles… I seem to see a lot of beer drinking unicyclists out there…
I only mention this because it seems strange that such well balenced people can love beer so much.