It's so great to see you try new things – and the game turned out more than fine!
I hope you liked working with Unity and we'll see more of your games made with it in the future (especially since Flash ends in 2020 :) ).
I dig the little details like items moving to your inventory when you collect them, the interactive rotating cube, or the animated menu. You could also make the "orange levers" animated, too, so they would move gradually, instead of just shifting to position.
One thing I'd suggest about 3D adventure games, though – add a way to highlight interactive items. There's a lot of detail in the background and literally anything could be interactive (doors, windows, posters, mailboxes, plants, cocktails…). Add an outline ("outline diffuse shader") on mouse hover, show its name in the text box, change the mouse cursor to "hand" (Cursor.SetCursor)… anything.
But it's not fun to have to click on everything in a scene. I've said it about your "asylum" games before and there, the objects usually seem out of place somehow (different perspective, size, lighting)… here everything looks like it fits in the scene and the collectable/interactive items just don't stand out.
The text is a bit blurry. Perhaps it's because it's resized, perhaps there's a wrong filter used. Would this help?
Or try TextMesh Pro which renders the text in a better way and allows you to use more complex text effects:
Also, I'd try antialiasing to see if it improves graphics. For example, the policeman has jagged edges which don't look too good when he's moving. Post-processing effects can also help you improve the overall feel – if you wanted more vibrant colours, for example.
I'd fiddle with the shadows settings in Graphics and on your lights, because now some objects look like they're floating – see the postbox. The shadows should start where the objects touch the ground.
Ambient Occlusion effect might also give the scene a more "natural" feel.
And finally, it's absolutely possible to add medals and scoreboard to Unity games… I've done it a couple of times before. You need to enable the new API in Project System and then continue from here:
There's a working example for unlocking medals on the page. There's no scoreboard example, but it's very similar to that.
I wrote more than I thought I would, I hope it was helpful. :)
Good luck with your future games! I'd love to see a low-poly asylum game at some point. :)