The temporomandibular joint is by far the most complex joint in your body for the reasons listed above. In addition, the dire ramifications of TMJ damage are further complicated by various inadequacies in TMJ research, dx, tx and management.
Currently, here are over 50+ treatments for TMD that range from conservative splint therapy to irreversible surgery; none of the treatments have been supported by the ADA nor AMA. The biggest problem with TMD is determining the cause. Most doctors/dentists make the haste assumption that stress and anxiety is the major contributing factor, meanwhile ignoring literature and patient histories which point at joint disease (e.g. osteoarthritis, rheumatoid arthritis), genetic factors, poor dental work/orthodontics, trauma, malocclusions, etc. TMD is poorly understood and creates painful manifestations in the jaw as well as it's associated muscles. Thus making daily activities such as talking, eating, chewing and laughing very difficult.
According to the NIH, nearly 11 million people in the US suffer from TMJ problems at any given time. Oddly nearly 90% of them are women. Unlike your knee or hip joints, implants/surgical replacements have been unsuccessful; many patients who opted for Vitek implants in the 80s (the so-called "TMJ cure!") had problems such as facial paralysis/disfiguration, bone deterioration, weakened immune system, etc. After seeing the consequences, the FDA banned Vitek in the 90s. Yet, by that time, nearly 26,000 Vitek implants were sold to oral surgeons. As for the "malocclused"-TMJ patients, orthognathic surgery has shown little success in subsiding TMJ pain. Many patients are talked into performing surgery to alleviate their TMJ pain yet end up as life-time surgical cases with additional problems.
So is TMJ a complex joint? I believe so. I probably went far beyond the OP's inquiries. I apologize. I just find TMD fascinating.
And, one question...
Is there any other residency/specialty other than OMS where one could learn more about TMJ? According to literature, surgery has been unsuccessful in many cases and is often considered the last option. So, I would find it odd if there was only one (pro-surgical) route supplied by academia.