You can kind of answer your own question, with a little basic knowledge of anatomy and the mechanics of Muay Thai. The best way is to break each movement down into their component muscle groups.
Feet/Calves/Shins - I group these together as many of the tendons and muscles for both run through the same area. The calves and other extensors are used to "bounce" while sparring, and to extend (point) the foot for some kicks. When you are doing kicks where the striking area is the ball of the foot, then you use the shin (flexor) muscles. Depending on foot orientation (My feet are somewhat duckfooted, which emphasizes medial development), then you may notice more development to the medial (inside) or lateral (outside) area of the calf muscle (Gastrocnemius/Soleus)
Quadriceps/Hamstrings - These would be utilized for kicking, obviously. Any kick that extends the leg from a bent to a straight position (front, round) or brings the leg forward at the waist (Many shin/knee/side of leg targeted straight leg kicks) will utilize the quadriceps more, while kicks that bring the leg backwards or from a straight to a bent angle (wheel kicks, hook kicks, axe kicks) will emphasize the hamstrings more.
Glutes - Almost any kick will utilize the gluteal (butt) muscles, but kicks such as back kicks, donkey kicks, side kicks will use the gluteal muscles for the majority of their power. They are also used for movement and stabilization.
Abdominals/Obliques/Lower back - These muscles are all used extensively as an anchor/base for almost all techniques, as well as adding rotational force to any technique.
Pectorals - Punches and similar motions (spearhands), and normal (As opposed to upset) ridge hands, some elbow techniques. The primary function of the pectorals is to adduct (bring into the center) the upper arm. There isn't going to be much more involvement for the pectorals than that.
Triceps - Extension of the arm, so any movement that takes the arm from bent to straight will utilize them. Punches, hammer fists will be primary among these.
Deltoids (shoulders) - Used for stabilization, and to contribute to any arm technique. Front/medial will be used more for the active motion (such as a punch), while medial/rear will be used to bring the arm back to the body after the execution of a technique. Can also be a primary motivator in some elbow techniques
Biceps - Retraction of the upper arm, and any technique that brings your arm from straight to bent, which is somewhat limited, mostly being back/reverse elbow techniques.
Neck muscles - Stabilization of the head, either to resist motion when struck, or as a base for other movements.
Upper back (Latissimus) - The primary function here is also adduction of the upper arm, in a different plane than the pectorals. The major involvement here is going to be a lot of the reverse arm techniques, and back elbow type strikes.
Forearm - Mostly in stabilization and rotation of the lower arm during punching and blocking techniques.
Stabilization - For martial arts, pretty much every muscle in the body will be used in some form or another, (see this question: What are the primary muscles worked when hitting a Heavy Bag?), so to find deficiencies, you need to look at what the activity promotes. For example, tae kwon do is very heavily leg focused, so to balance I would have the practicioner do more upper body work.
For muay thai, it is a very intensive, full body art. About the only places I might see weaknesses are the biceps and the lats, as they are underutilized for their comparative size. Your lower back may be comparatively neglected as well, depending on what calisthenic type exercises you do. However, if you heavily favor the striking side of muay thai, then your legs may be comparatively weaker, and vice versa if you are primarily a kick oriented fighter. Overall, I would say that muay thai actually is one of the better arts for full body development, and there wouldn't be much to supplement for, unless you notice that you are lacking comparative power in certain techniques, that one portion of the muscle is being more developed than other (Such as the medial portion of the calf as opposed to the lateral portion).
The one other caveat, is that muscular development can come at a cost, either in mobility, flexibility or speed. If you do add in weight training, make sure to still emphasize speed and flexibility work. If these are neglected, then weight training over time can restrict range of motion, and possibly change muscle fiber composition to a small extent.