At a quick glance, my comments are:
- The first thing I noticed is lack of a filled GND plane. That's the first thing you should do, typically on the bottom plane.
- Power traces should typically be a bit thicker than the signal traces, and they should route power in a star-like formation. They should not snake around.
- Similarly, some signal traces look like they are routed over a way too long path than they should be, and they are switching the layers too often. Perhaps reroute them in a similar manner - a star-like formation instead of a snake-like pattern. The board looks like a labyrinth.
- U1 could probably use a 100nF decoupling cap close to its Vcc and GND pins.
Happy PCB'ing!