- For a board so big for the components it has, IC1 sits uncomfortably close to the edge (it almost falls off!)
- I see two big power transistors with only narrow traces from their pads.
But of course Matt's remark about the missing connectors to the outside world is the most important one. It's obvious that you'll need those to use the board, but they're also important towards layout.
I always try to draw my schematic in such a way that the current flows naturally from left to right (i.e. without making too many unnecessary turns), and use that as a basis for the PCB layout. So you either place all connectors on one side, so that the current follows a "U" shape on the board, or you place them on opposite sides, so that the current flows from left to right (top to bottom, whatever).
It's your first board, not too many parts, so you can afford to space them like you did. But even with the same dimensions I would place them closer together. It's good practice for the puzzle that component placement will become in future projects, and for some components, like decoupling capacitors, it's mandatory. Exception to the "cozy together" rule: power components need room so that they can drain their heat and that it doesn't go to other components which will not like it.
Placing them closer together in the center of the board also leaves lots of room for mounting holes, which you don't have now. I usually drill 4mm holes for M3 bolts.
Talking about power. On your schematic mark the nets which carry high currents (some EDA software allows you to use custom net colors or widths, I don't know if Eagle has this feature). Use wider traces for those nets on the PCB, even if you only need 500mA. You can afford it.
Then there are the details Matt also referred to. Like the vertical trace going from IC1 to R1. If you move it a few mm to the left you can get rid of the superfluous 90 degree angle near R1. Also the vertical traces on D1's anode: try to let them run in one line, without unnecessary turns.
And nobody seems to know exactly why, but the 90 degree angles are almost always chamfered to 45 degrees. May have to do with aesthetics ;-).
And lastly, keep high current (and high frequency) traces short. Don't let them run all over the place. Again if your EDA software supports it, use custom colors for the high current traces. You'll see immediately where you can optimize.
The advice to keep traces short may seem contradictory to letting it flow from left to right, but the point is not to let traces make unnecessary twists and turns. For a power application it's probably best to have input and output connectors next to each other, and the transistors nearby.