2 Layer Through Hole PCB
First, you should make the power traces much thicker. I use at least 70 mil thickness for my power traces. In the best of worlds, you can have the board made with 2 oz or thicker copper plating, but generally, that's very expensive. Panelized board orders, which is what hobbyists can afford, are almost always just 1 oz thickness. (oshpark.com or iteadstudio.com or seeedstudio.com are some of the lower cost ones) I'd recommend oshpark.com if you can wait 3 weeks for the board, and iteadstudio.com with DHL shipping if you need them within 10 days.

Second, you probably want to re-lay-out the components so you don't have super long traces crossing the board from your power transistors to your diodes to your connectors. Keep the diodes close to the connectors, and the transistors close to the diodes. Even with thick traces, there will be some loss (which turns into heat) that you want to minimize by keeping the traces short.

Third, in Eagle, the rectangle tool cannot be used to generate a ground pour. You have to use the polygon tool, and draw a rectangular polygon. Do that, name the polygon "GND" and hit ratsnest to see your ground pour appear.

Fourth, it looks as if you want to put high currents through pin headers. I don't know how high the currents will be, but if it's more than, say, 2A, you likely want to use screw terminals rather than pin headers. High-amperage screw terminals typically come with 3.5mm or 5mm (or 200 mil) spacing rather than 100 mil spacing like pin headers.

I once mis-soldered a board and attempted to put > 12 A through a 16 mil trace. Luckily, that trace burned off and worked great as a fuse :-)

Regarding the ceramic 0.1 uF capacitor close to the microprocessor: That's known as a "decoupling" capacitor, and one should be placed as close as possible to each chip you have that could be switching at high speeds. These capacitors serve as "reserves" for high speed switching, reducing the EMI introduced on traces further out from the chip. Using ceramics is important because of their very low ESR -- an electrolytic has a significant ESR (often in the "ohm" range) which makes it become an RC filter which means it can't respond quickly enough to near-instantaneous changes in current draw.