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This is just an informal observation, but I tend to find that the ported apps on OS X that don't feel right are the ones with too much clutter - multiple panels along the top, down the bottom, and particularly a reliance on toolbar buttons. (That's aside from getting the fonts and button sizes, etc, "native".)
One example among the apps I have here is Evernote (could be an old version - 1.10.1 - don't use it that much), which uses the right widgets and looks and all but feels cramped for a Mac app, with a login-type of bar under the toolbar, three vertical panes, three panes in the leftmost one and three toolbars in the rightmost column where you type text.
This sort of thing can feel awkward, or foreign I guess, even where it isn't extreme.
From the screenshot you've included in the article, your interface looks simple and lovely. Even so, I'm not sure how the "Add, Show, Tools..." strip of menus would translate to OS X. The bottom panel of track information may or may not work as well.
Among other tiny points (but I suppose the minutiae are what you're canvassing) is the volume slider, which is obviously a volume slider and everyone would recognise it as such, but without any icons or other friendly signposting, it appears to me to have a whiff of being a bit of a technical apparatus, in terms of aesthetics anyway. The icons of sound files next to the tracks in the main music library list would be out of place on Mac desktops too, I would think.
I suppose, though, with these look and particularly feel questions, it's hard to know unless you take a whirl on it to get a feel.
You're brave to seek help so openly. Good luck.
Thanks a lot! Your post is a gold treasure full of good points. Awesome.
I think the Add, Show, etc would go into the global menubar perhaps?