Well, the board IS ready for production, and it WILL work, but it's bad, sorry.
If your goal is to learn something or try out something then AVOID THE AUTOROUTER, fiddle around with the board, spend a day or so trying a better layout etc. While not critical, try to use different line widths for different signal kinds (thick for power, slim for signal). Play around with the layout, add some mounting holes, change the board shape/size, try different trace types... also, you can do this in one layer.
Also, at least a small power decoupling cap (capacitor parallel to the power) wouldn't hurt.
Also, look at your solder mask - it's the green stuff. I assume that you wish to contact the battery on the circular patern on the PCB - you have a trace going through that uncovered area.
Also, be mindful of the orientation of your SMD battery holder and think in 3D - unless I'm mistaken, the user will have to get past the 555 and misc components in order to insert the battery into the holder the way it's currently oriented. Make sure it's oriented with an insertion direction facing outside of the board.