The trade situation seems complicated, but the real complexities and dangers of Brexit lie in its effects on services. The agreements here are domain-specific and range across a huge range of areas — nuclear energy, chemicals standards, and so forth — but I've been reading a bit about aviation, something I hadn't originally considered would be affected at all. Here as elsewhere, the Financial Times' coverage is much scarier than that of the Guardian...
The creation of the European Common Aviation Area (ECAA) in 2005 and increasingly uniform regulation across Europe, guaranteeing open access to routes and landing rights, has underpinned the rise of low cost airlines and cheap flights. Along with common safety regulation through the European Aviation Safety Agency, it has also reduced the regulatory burden for aviation services companies. The UK has been one of the strongest advocates of increasing integration here and its companies have benefited more from it than most. (There have been, as always with this kind of opening up, losers: airlines that only survived through monopoly relationships with airports or state subsidies have failed, along with companies that couldn't cope with increased competition, and so forth.) The UK is, through Heathrow and its low-cost airlines and aeronautical firms, a major air services hub.
There is precedent for the UK being in the ECAA without being in the EU — as with trade, this could also be called the "Norway" option — and if that happened there should be no major problems. But this would require accepting European aviation law and the ultimate arbitration of the European Court of Justice on aviation matters (and Gibraltar may be a spanner in the works)... Even membership of the broader Common Aviation Area (CAA), along with Israel, Moldova and Morocco, implies the adoption "of the part of the Acquis containing the European aviation rules, starting with safety requirements". The Euratom precedent suggests this may be unacceptable to the current government.
Again mirroring the situation with trade, the UK could fall back to what we can call the "Switzerland option", with a separate bilateral agreement with the ECAA. But this has serious limitations. Swiss airlines can only fly routes that leave from or arrive in Swiss airports, most obviously. And the UK would have to create its own regulatory authority, or expand the Civil Aviation Authority (perhaps on a smaller scale than the ECAA, but we'll be paying for 100% of it instead of just part of it). And any airline operating in both the UK and the rest of Europe would now have to deal with two regulatory authorities instead of one. Such an agreement would also need to be negotiated in the two year framework — along with (among others) a UK-Morocco aviation agreement to fill in for the existing ECAA-Morocco agreement, a UK-US agreement to replace the existing ECAA-US one, and so forth. There's at least a small chance of things going very wrong here: as Ryanair's boss puts it, "a remote chance of all flights between the UK and Europe being suspended in March 2019".
Similarly, if the UK remains a member of the European Aviation Safety Agency and enacts its regulations, there should be no problems there — except that EASA regulations are European law, and the UK would now be subject to an EU body and EU legislation over which it will no longer have any oversight. If it doesn't, then it will have to request certification as a "third country" for its aeronautical industries from the EASA — or all the companies currently providing services to European airlines are going to need to relocate.
"The EASA, rather than Member States, was also entrusted with
the responsibility of issuing certificates. For instance, the
EASA is entirely responsible for the certification of aircraft
types and other aeronautical products. The EASA also issues
certificates for organisations located in third countries. The
national authorities of Member States however continue to issue,
under EASA monitoring, individual certificates to aircraft and
most organisations and personnel located in their territories. All
certificates issued on the basis of EU law are valid in all EU
Member States, which guarantees a uniform level of safety for
the traveling public and a level playing field for operators."
With air traffic control, some people just assume the UK will remain in the
ECAA and "commit to full and continued compliance with EU law", because the alternative is too horrible.
"provided the UK commits to full and continued compliance with
EU law – over which we would genuinely have no say – we
should have no particular difficulty ensuring continuity of air
... it is inconceivable that the UK could stand apart from
the European Common Aviation Area, while it is scarcely
possible that anything else would be on offer from the
Commission. The UK will either have to bite the bullet, or
face the prospect of terminating flights to and from mainland
Europe (and even overflights over the ECAA territories,
including Norway and Ireland). The alternative is to broker
an entirely new agreement under the aegis of ICAO, with all
the attendant complications of having to start from scratch."
There are no obvious gains to be had here at all that I can see. The UK is most unlikely to be able to negotiate better third-country deals than the ECAA has, and the benefits of having unified regulatory and safety regimes across Europe seem clear-cut.
Whatever happens,the UK is going to get more government bureaucracy here, not less, and its airlines and aviation services companies are going to face more regulation, not less. Also, I'm willing to bet that we end up with ultimate arbitration mechanisms that are vastly less transparent and open than the European Court of Justice.
Update: I no sooner post this than we get this story: "UK-based airlines told to move to Europe after Brexit or lose major routes".