The source is one of my all-time favorite songs.
THis is definitely an interesting take on it. Sort of a laid back piano/guitar jazz thang; I'm definitely digging it.
I'd make the guitar a bit quieter and add a touch more reverb; right now it sounds like the guitar amp is right next to my ear, while the piano is in the next room.
Noticable mistakes on the guitar at 1:35 and 1:43, but I assume you already knew about those.
As far as production goes, it's difficult to tell what's intentional and what's not; the piano is really bright and the guitar really dull, but to a certian extent that works with the style. The whole thing is very minimalist and my first impulse is to say that it needs bass, light percussion, and perhaps pads of some sort, but again, the minimalism sort of fits with the style, and adding other instruments could well destroy the charm that makes this mix so captivating.
I think it could do with some more movement earlier in the piece. It's very slow and laid back, but that gets old quickly without any spice. This could work as just a guitar/piano duet, but you'll need to do a bit more to keep it interesting. It sounds like between guitar and piano, piano is your forte (forgive the pun), so I'd focus on spicing that up a bit. I'd love to see the piano take center stage at some point in the mix with the guitar sinking into the background; perhaps this could be done in the next section (I assume you were planning on making this longer than it is now).
There are a few points where the chords on the piano sounded a bit wierd to me, but I don't know enough theory to say why they sounded wierd or how to fix it, and it may well be intentional anyway.
I'd say for a first mix, you're off to a very good start.