Uplink uses all of my screen on OSX (MacBook Pro Retina 15''), but the text in the upper left corner is displayed in a small box and it doesn't fit it. The issue is visible on the attached screenshot. I can't do anything. It happens right at the start, before registering an account.

Im running the latest version of OSX 10.9.2

Any help?

I don't have a Mac, but it looks like an incompatibility with Retina screens - the text isn't supposed to be scaled like that, and Retina is a thing that will do just that.

Judging by this Apple Support article, you might make it work if you configure the application to start in Low Resolution mode.

Also, if you haven't already, be sure to contact support - and if the above idea works, tell them that too, so they can try to fix it in general.

I also have a new macbook running 10.9.2 and had the same problem. Here is what i did:
Hit cmd+f this will switch from fullscreen to windowed-mode. There you should be able to see the buttons and normaly register an account.
Once you are in exit to the main menu and go the graphics options. Make sure fullscreen is unchecked, then exit the game so the settings are saved.

Ever since then i have been playing the game in windowed mode without any further problems.

Yep, works fine in windowed-mode.
In the app store, however, there is a more recent version (1.6.8) that supposedly fixes the resolution problem with retina macs. I think it would be awfully nice to have that update on GOG as well.