Fist impressions can never be reproduced, so I'm typing this as I go along:

1) Welcome dialog is... out of place. The design is not consistent with Apple UI guidelines, I can't tell the three options are buttons.

2) The cancel button on the welcome dialog looks like an odd man out. It's just floating there in the center, and I think the caption (cancel) is also something you can improve.

3) I think the now-playing thing in the sidebar needs to be pushed down by ~60 pixels, basically starting under the main bar across the rest of the screen. It's not very symmetric the way it is now. You should also have a divider between the close buttons and the now playing section - see Chrome.app for a good example of doing it smoothly.

4) Playlists: now change when I hover over the entries, I was expecting them to go blue. Clicking on them has no effect, I must double-click. non-intuitive.

5) I love the statistics and charts in History, but I wonder if the name is accurate? I'm seeing a breakdown of my music collection, but the only "true" history tab is "Recently Played" which is also given the least prominence.

6) When starting the app, the whitespace stretching from under the now playing section to the bottom of the screen in the sidebar is jarring. It doesn't look nice empty, I'm assuming something will show up there at some point in my playing around with it.

7) Playlists uses an entirely different UI from Library. I like Library's detail view drilldown. I think something like that should be used for the playlists too. See point #4.

That's all for now. May update later with more feedback.

Good work. It looks very promising. I love that it's fast and not-bloated.

EDIT:

No way to turn off Growl messages? Oops.

EDIT:

Add Playlist -> then press esc. The playlist gets added anyway with the default name.

Playlist list needs right-click functionality, even if it's the same menu that shows up when clicking the cog. Don't disappoint your users expectations as to how an interface will act.

EDIT:

Playlist tab's "Add Playlist" pretends to be a tab but it's actually a button. Very confusing. Don't do that - buttons are buttons, tabs are tabs. Even if they're right-aligned.

EDIT:

I think you have a bug when you turn on repeat and shuffle in the middle of a song. When the song ends, it will be repeated immediately, then everything works out.