Maintaining the build systems, compatibility layers and so forth won't be easy (Adobe often couldn't manage it), and bug fixing in the code is a risky prospect for preservation as it could render older content unplayable or differently playable.
The swf file format is almost open - it would be nice if Adobe updated the published specification to the latest format. Again that would go some way towards ensuring the content remained available in some way.
Edit: genuinely interested in the downvotes here - am I missing something fundamental about content preservation? It seems logical to me that the file spec being available + original players is far more valuable than the source, as the source will then bitrot without continuous maintenance. In comparison the players will always run in the VMs.
AIR did hold promise, but ultimately suffered from being terribly cumbersome to extend when you wanted to access native features or platform standard libraries (I've created several AIR native extensions over the years).
However, one of the big problems with using Flex or AIR after Adobe have end-of-lifed Flash is that you're going to lose access to the content creation tools. There are some alternatives (FlashDevelop and FDT for coding, I forget the name of the attempt at an open source Flash timeline editor), but nothing is close to being as good as Adobes own tools when you want to.
If you want to leverage knowledge of ActionScript, people may be better off looking at something like Haxe for cross platform gui app dev.
For the drop downs - when I used Flex I had the same issues over window bounds, in that nothing could extend beyond the limits of the flash rendered window. Did they fix that in later versions?