Good point on the decoupling caps. Not sure how I missed that - the board design as posted will not work, as it omits the necessary decoupling caps. Vcc to Ground next to every power pin on every digital IC, traces kept as short as possible (between the Vcc pin of chip and cap, and between Gnd pin and cap). I have had problems when I had an inch between the decoupling caps and power pin. Without decoupling caps, microcontrollers may reset or hang in response to changing load (for example, turning on an LED with a microcontroller I/O pin, or writing to the flash) and are more sensitive to external interference.
And the regulator needs caps as specified in the datasheet (note: regulators are often very picky about their caps. Some need ceramic or tants only, some need electrolytic, some just spec the ESR which in turn dictates what kind of caps you can use), otherwise it's not going to behave as a regulator, but an unstable oscillator.
And yes, this makes routing it on a single-sided board really hard. That (along with how cheap it is to get boards fabbed) is why we all use double-sided PCBs!
As an aside, where the heck do you get 10 pcs 100mm x 100mm for $5? My board house charges $17 for that!