I've recently submitted to the Mono team (and had accepted) a few patches to fix the issues I've found running BlogEngine.Net under Mono on Linux.
At this point, you will need the very latest Mono release (r102737) from SVN to get the fixes. These fixes are for Windows/Linux interoperability, cross directory master page & user controls, and Forms authentication.
With these fixes now applied, I now know of no problems with Mono running BlogEngine.Net on Linux. (I say "know of" because I haven't tested everything yet).
No problems with Mono, but there are problems with BlogEngine.Net.
The BlogEngine.NET code makes a number of assumptions (like a Dictionary will retain the order of items that are inserted) that aren't part of the .Net runtime's specification. I have 3 issued logged in BlogEngine.Net's Issue Tracker on CodePlex. All of the issues I've reported include the code changes required to fix them. Three weeks later, and they still sit there. There are three weeks worth of issues between mine and the latest one resolved. I expect we'll see them applied in about three weeks.
But on my system... all problems appear fixed.