1) When your PCB is done measure your current to get you battery drain current. You can calculate this with some of Dave's other videos or ask how to get mAh.
2) The forth (what I think is a cap) on the bottom doesn't appear connected to anything on the left side. Use EAGLE's DRC and ERC they work very well.
3) The ATMEGA8 pad layout doesn't appear to be correct to me. The separation between pins in your image for the bypass cap on the left side appears blended and shorted.
4) The multiple traces from the battery negative should be a big pour in the PCB. Use a poly in EAGLE to connect this.
5) Even if you aren't doing a silk screen don't let the images overlap.
6) You have two different pad types on the anode and cathode of a diode.
7) The 100 uF main bypass is probably overkill.
I'm not sure why there is a pad and through hole just above the main IC.
9) The silkscreen should always contain the part numbers, R1, C1, etc. Even if you won't use a silkscreen. This is also necessary for design reviews and just to get in practice for it later. And then use the EAGLE renumber board feature to set the numbers after laying out the board on the X - Y axis.
10) The copper circle under the ATMEGA8 seems unnecessary.
Recommendations:
1) Use a two layer PCB. Even if done at home. Positive resist PCBs are cheap to buy and the small fish tank plastic etching kits with Sodium etchant work really well. I have used Ever-Muse boards I'm not sure if they are still made under this name. It's easy to line up the photo images even double sided and there are probably tons of videos.