The ship's hit box is off... it seems to include the nose of the ship and some empty space out in front, but not the back half of the ship. Makes it hard to dodge shots when you can't tell what you need to avoid.
The gravity mechanic is a nice change from the usual flying-in-straight-lines mechanic. A couple comments: it looks like a circle's gravity field stays behind after I collect the circle. It can be hard to tell which circle is larger when they're close in size, so it'd be nice if there was some other indicator (color, outline...) or maybe you just bounce off of circles that are that close in size.
It seems like weapon and speed upgrades carry over from one game to the next. I finished a round on easy, and when I started a new game on normal, I could move fast and had the same weapon power I finished with, but the upgrade slots were empty. I upgraded my weapon fully after that, and lost the ability to shoot.