The "potential problems" are different for international passenger business vs everything else, from what I have read. Whilst non-international transport requires that UK develop its own regulatory regime, international transport has more of a problem.
Currently, airlines based in / authorised and regulated by a country that is a member of the Common Aviation Area (I can't bring myself to use CAA for that), namely EU Member States plus some neighboring countries like Morocco, Iceland, Norway and Switzerland, may operate air routes between any airports located the Common Aviation Area. For the UK to remain a member of Common Aviation Area and therefore benefit from the European “Open Skies” requires that UK accepts the freedom of movement principle and acknowledges the jurisdiction of the European Court of Justice. See the problem?
Earlyin 2017 airlines were cautious about what the future might hold, but that has given way to “contingency planning” for a "no deal" scenario.
On 2 January 2018, Ryanair confirmed that its subsidiary, RyanairUK, had filed an application on December 21 for an air operating certificate (AOC) with the UK’s Civil Aviation Authority. If granted then Ryanair (the existing company) will not be able to fly routes between UK cities post Brexit, but Ryanair UK will, and so the affected slots and routes belonging to Ryanair will need to betransferred into Ryanair UK.
It is not just Ryanair: in October 2017, Wizz Air appliedfor a British AOC. Going the other way, in July 2017, the British airline EasyJet applied to Austro Control, the air navigation services provider controlling Austrian airspace, for an AOC and to Austria’s Federal Ministry for Transport, Innovation and Technology (bmvit)for an airline operating license. It will create a new airline, EasyJet Europe, headquartered in Vienna, that will operate flights both across Europe and domestically within European countries after Brexit. Currently those slots /routes all belong to EasyJet and these will need to be transferred or made available to EasyJetEurope.
Simples! (not really)