Election schedule for the five potential countries who might do the anti-EU referendum:
Finland: Parliament (Spring 2019), President (Jan 2018)
France: Parliament (Summer 2017), President (Spring 2017)
Germany: Bundestag and Chancellor (fall 2017)
Austria: Under debate by the court if the Presidential election must be redone, Parliament (fall 2018)
Netherlands; Parliament (spring 2017)
Hungary: Premier and Parliament (Spring 2018)
EU Parliament: Spring 2019
If the UK treaty to leave the EU were to take 12-to-18 months....it would easily affect three of these countries as a minimum. Just having another 10-percent of voters go right-wing and anti-EU in France would shift the Presidential election around a good bit. The same could be said in Austria....if the court deems the May election as a screw-up.
Having Scotland push for a leave-the-UK referendum and get results by October (my best guess on how quick this could occur)....would mean that they would try to come in and apply for EU membership by the end of 2016. Would Scotland be automatically accepted into the EU? That's the puzzling part of the situation....any number of the present members could raise concerns and delay this application (not just a year, but for several years). So you could envision the Scots standing there in the spring of 2017.....having gained independence and then finding the door not fully open and a three-year period of waiting for members to review their application and agree to allowing them to join.
The Gibraltar crowd, the Northern Ireland crowd, the Wales crowd, the London-City State crowd? Yes, all the same. In fact, there's zero chance that the Gibraltar folks will ever be accepted as a member of the EU as long as Spain as a chance to deny them. In the case of both Wales and Northern Ireland....the question will be if they have sufficient funds to run a government, and opening of their financial books.....which might not be a pleasant situation. In the case of London.....the EU members would be questioning the idea of city-states into their organization, and if this were inviting future trouble (what if Vienna wanted to be an independent nation, or perhaps Amsterdam).
If you were looking for a rather comical mess where some people felt they would get preferential treatment to join the EU.....well.....this isn't it. And I can imagine some Scots sitting there in a powerful fit of anger and frustration....that they weren't given a front-door welcome as they anticipate.