Short version (for the tldr crowd):
It's very important from risk management reduction strategy, for all physicians, to stay comfortably within your scope of practice and to be in close consultation with a healthcare attorney, when setting up practice arrangements where there are potential Stark and anti-kickback issues to be worked out.
Long version:
1) *The below is not legal advice. I am not an attorney. In fact, consider everything below, wrong. Ignore it 100%. Stark and anti-kickback law is complex with subtleties and gray areas, and on some issues, even the attorney's don't agree. For legal advice ask a healthcare attorney your question and ignore me completely*
However, here's my answer, having had some exposure to these issues in the real world.
Seeing a patient in the ED then in your office is absolutely not a stark violation. Surgeons and all kinds of ED consultants consult to the ED, see a patient and then arrange follow up in their office. They then see the patient and bill for both visits. It's not "illegal self referral" nor would it be for a FM doc. There is no referral happening. It's simply continuity of care. It would not be any more illegal for an EM physician to continue care with a patient on an outpatient basis, if he had a primary practice location in which to do so, than it is for the ED consultants that do this routinely.
However, the anti-kickback and anti-self referral laws prohibit you from referring to a facility other than your primary practice location, where you're not seeing the patient and doing the actual work, where someone else is, and sending you money in return.
Example 1: Surgeon (or EP) sees a patient in the ED. He diagnoses diverticulitis, determines the patient is not sick enough to be admitted, and prescribes outpatient antibiotics and arranges follow up in the clinic. The then bills the patient for the ED evaluation and the outpatient visits. That is 100% legal.
Example 2: Surgeon (or EP) sees patient in the ED. Same situation. ED consult. Arranges outpatient follow up and bills just like example 1. But in thte process he refers the patient to an imaging center for a CT. (So far, totally legal). Come to find out, the surgeon owns a 50% share of the imaging center and is getting money for each CT. That becomes illegal, because he's referred outside of his own care and is getting a kickback for an outside referral. Interestingly, there is something called the "in office ancillary exemption" where it becomes legal, if that surgeon possess and owns a CT scanner in his office, under the same roof as his primary practice location, and bills for the work of doing the imaging. This is what allows ortho/neuro/neurosurg/pain practices to have their own MRI machines in their offices, and bill for it legally. Also, some larger primary care offices had labs in their own offices and bill for it. That's totally legal. If it's off site however, and you own all or part of the lab and "refer" out to it, it's not legal.
So, in your example of the EM trained FM doc, seeing a patient in the ED, and following up in his outpatient office, that's totally fine. There's no referral occurring; it's simply continuity of care. If, on the other hand, he refers to some outside office, doesn't see the patient himself (therefore a referral must be generated) but secretly he has some part or total ownership which provides his monetary compensation for that referral, then that likely violates Stark/anti-kickback law. Even if the patient is then seen by a PA or NP, that he officially supervises, it still may be okay. Some other facility, with another doc's PA where your doc somehow has ownership or gets sent a $ spiff for each referral without ever seeing or supervising the seeing of the patient? Not okay.
2) I know several EM docs that have transitioned to FM. It's definitely legal. While I don't think it's ideal (much like FMs doing EM) I think the specialties are close enough, it can be done done by a smart, motivated person who undertakes a tremendous amount of self study to bridge the knowledge gaps. But you must be prepared to detail to a medical board or jury, exactly what that self study was.
3) There is no law that prevents an EP or any other physician performing Moh's (or any other) surgery, however medical boards tend to take a very unforgiving view of this when there's a bad outcome. It can easily be considered out of the scope of your practice and suddenly becomes very hard to defend in a malpractice case or medical board hearing if there's a bad outcome. Since there's enough overlap between so many specialties and so much change an evolution in treatments in standards of care, it's therefore impossible to criminalize all cross-over between the scopes of different specialties. Medical boards are left to judge these situations when there's a bad outcome. It's a less than perfect system, but it's the best one we've got.
As an aside; one of my good friends is a Derm/fellowship trained Moh's surgeon. He does facial resections, skin flaps, skin grafts and even reads his own path. He's a rock star. I'd never even attempt to do this work with an ED background and without some other background in either Derm/Plastics and/or Path. I'm not saying it's impossible, but it would be extremely poor judgement if I were to do so. Is a 1 month Derm rotation where ones does a lot of Moh's enough to be competent, when Dermatologists spend a whole year in fellowship learning the technique? I don't know for sure, but it seems like a stretch to me.