I'm going to postulate three separate problem areas each deriving straight out of the two accidents and their massive aftermath.
First is the need for some approach more credible and authoritative than what appears to be running at present, for purposes of returning the aircraft to airline service. The FAA has the leading role at this juncture but the other CAAs who also are evaluating the reconfigured (or perhaps some other verb is more technically sufficient) airplane will have their own point of view based on their own testing. The international system of certification and acceptances by other CAAs has broken down, hasn't it? - and to be replaced by what? As a subset, the process on this aircraft's return to service, to date, does not seem to have warranted a resurgence of confidence in the FAA. The looming reform legislation (probably in the next Congress after the November election, not before) will try to address . . . where to start?
Then there is the problem of the Boeing boardroom, top management, and culture. There is no shortage of recitals of the tale of how the company drifted away, or was pulled away, from its roots in excellence, if not superiority, in engineering. Less prevalent are sober gameplans for restoration. Cleaning house is the oft-recited solution kickoff, but to be followed by what, exactly? This is not to say those who tell the story of the long-term decline of the company have no plan other than to try to turn the clock back, one mistake of the past at a time. It is to wonder what is the gameplan to make Boeing 2021 a company at least on the road to restoration.
Not least, the problems of the 737 MAX appear closely linked up to the growing role of automated systems in the control of transport category airplanes. The proliferation of systems which can control flight with limited or no pilot input can create new problems, or so the MAX crashes would suggest: things were happening too quickly and in too complicated a manner for the knowledge and abilities acquired in training to be sufficient. Of course that is not a statement of all the causal factors (like, uh, MACS wasn't a known entity whatsoever to the pilots) but it is factual (correct me if I'm wrong). And won't this mismatch get worse? - as more cockpit automation intersects with pilots who get type rated but without having acquired much (let alone a lot) of airmanship instincts.
(Two big problems not listed here because I think they're connected to the MAX situation but not about the MAX as such: the corporate governance model and whether so-called "stakeholder capitalism" would make any difference, good or bad; and what kind of magic will it take to restore the airline world to something akin to pre-pandemic levels of operation.)