[Advice needed] Building a small BCD clock.

Alright, hope this post isn't too old yet, because OP is here to deliver... Somewhat.

So I got this set up on a breadbord with the Arduino Uno, just to see how the code works. I'm using the millis() function to count milliseconds from the time when the program started. Every 1000 milliseconds, it adds one to seconds, every 60 seconds it adds one to minutes and so on. Each LED is connected to it's own digital pin on the Uno and lights up accordingly with basic if functions. Right now there's only one button to set minutes on digital pin 0, but I plan to add one for hours as well when its time to shrinkify this project to the ATtiny2313. The reference page says that this millis() function overflows after approximately 50 days, how badly does this affect the clocks accuracy?

I'm building the schematic with Eagle now. Do I need any other components, suchs as caps, in order for the ATtiny to work properly?

Thanks for your help guys!

EDIT: Will the buttons work with the ATtiny? I wired them (Or "it" at this time) as instructed on this page.