This is a "me, too" comment.  With a few more pointers and opinions.

The problem is a not-so-minor regression for the Ubuntu Xenial distribution - it is very close to be a showstopper for my company for upgrading from Trusty to Xenial.  Monodevelop simply doesn't work with asp.net in Xenial.  I would heavily recommend that the importance of this regression be increased.  I would also like to assist in its solution, but whereas I know more that a little bit about building and maintaing debian packages, the complexity of the monodevelop package is a quite daunting ...

I can add that even though we only use LTS versions of Ubuntu for production we do try out the non-LTS versions - and this regression is between 15.10 Wily and 16.04 Xenial - monodevelop worked just fine with asp.net in Wily.

The problem is dead simple to reproduce, just take a Trusty or Wily monodevelop, create a new Web application solution+project - the one with a single button - build and run.  Works fine, then move it to a Xenial monodevelop, fails.

You can get a whole load of useful information by simply googl'ing the error message string "error: The ASP.NET add-in is not installed.".  Many different people, including some at Xamarin has observed the problem and commented on it.

Essentially, the consensus seems to be that the Debian/Ubuntu release of monodevelop 5.10.0.871-2 are missing some elements.   One widely recommended solution seems to be to download the "debianized" version of monodevelop 5.10.0.871 from http://download.mono-project.com - its version is 5.10.0.871-0xamarin2.  Installing that certainly solved the immediate problem for me - but I really prefer to work with a single, supposedly consistent, distribution.

Problem is that the -0xamarin2 is not that well integrated with Ubuntu Xenial - it seems more to  be a kind of "generic relatively modern Debian/Ubuntu packaging".  For a starter, the
sources to the -0xamarin2 simply fails build on a vanilla Ubuntu Xenial.  Second, there are problems with the nunit integration.

I have spent some time studying the difference between the Ubuntu (-2) and the Xamarin (-0xamarian2) sources.  Fortunately, both are using the same .orig.tar (which they should, of course, but it is nice to experience that packagers actually follow the conventions!).

Well, the differences are pretty big - a unified diff is about 3000 lines, and that is excluding the "Only in monodevelop-this-and-that" diffs.  One major difference is that the ubuntu version seems to consistently go for targetframework 4.5 in the .csproj files, whereas the xamarin version uses many different framework versions.   I speculate that in pushing the Ubuntu packaging to pure 4.5, it may have been necessary to cut a few corners, and one of those be ASP.NET.

Certainly one difference between the two packagings is in the file .pc/applied_patches where the Ubuntu has a new patch called "dont_bundle_aspnet_assemblies.patch" ... One of the things I intend to try out is of course to remove this patch and try a rebuild - I don't hold that much hope, however, the patch is probably there for a reason.

I (and my company) really need this problem solved eventually.  It is no big hurry - it is not that Ubuntu Trusty has stopped working :-) - but sooner or later, this regression will be a problem.  I would like to assist, within my limited competence - certainly I will continue to report here if I figure out something of relevance.