I didn't read all the above before writing this, but now I have, there seems to be some consistency, and good ideas. None of the comments below are requests for functionality. Just examples.
1. Generally Theatre View Skinning. Specifically, move, delete, add menus in Theatre View without breaking features, such as where to start MC. Ideally, the whole Theatre View skin would be user configurable with drag and drop fields, hidden fields if necessary with default values where required to make the rest of the skin functional. Sort of like a free-form, forms design tools, with element definition for groups of fields, reusable elements, all done in a GUI. Sort of like Microsoft Access forms, but not as clunky. I guess Standard View skinning may need some love, as per other comments, but I treat Standard View as the maintenance view, and don't care as much what it looks like, as long as it is fully functional.
2. Delivering "Play anything, anywhere, anytime". Plex was my second choice after MC, mainly due to the promise of this. I don't know if Plex actually delivers on the promise. JRemote may be great, but it sounds like it needs more work, based on other people's comments. I am thinking more of start watching on my TV, finish on an iPad or other (including Window 10) tablet sitting in bed. Or continuing to watch on my phone as I wait somewhere for something. Much of this can be done technically, using Webgizmo for example, but the functionality isn't a Competitive Edge. It is just a "oh, we can do that as well" followed by links to disparate bits of instructions. What is needed is Apps for all platforms that are standardised and fully functional.
3. The limitations of the current Client/Server implementation, which is actually a copy and synchronisation process mostly, means people have to learn a lot about what they can do on a Client, versus what must be done on a Server. I'm sure people who run the 30 day trial hit up against issues here, and decide it isn't the application for them. Competitors may fair no better, but your competition may well be "no decision" rather than selecting a competitive product. Certainly that was my decision for a number of years; I lived with no Media Center and just used discrete hardware.
4. Improve the Discovery process both within MC and using external links. More metadata stored and displayed for media, with links or inclusion of data about related entities. i.e. Actor/Director/Artist BIOS, click a link to see all movies you have associated with that entity, click a link to go to an external page on he entity, based on entity type. i.e. IMDB details for an Actor or Director. Also, built in Lyrics for audio, or simple plug in installation that works.
5. Out of the box whole house synchronised audio. Others seem to compete almost solely on this feature.