I found a horrible wiring bug that was preventing the hours digits from rolling over when they reached 24. Fixed.
I have one minor, or major concern depending on how you look at it: When I hooked up the 1 Hertz signal to a scope, the frequency displayed was 1.01 Hertz. I don't know if this was the fact that I was using a cheap scope ($50 from Amazon), or a cheap crystal, but I shall have to investigate further. I can't leave the clock running for too long without it freezing which is a result of a bad connection somewhere on the breadboard that I haven't managed to track down.
If anyone can think of a reason why the signal should be rated at 1.01 Hertz, I would be glad for some input, or pointers. Let me know in the comments section.