Here are a few quick suggestions:

1) Make sure both supplies are heavily bypassed to reduce supply transients.

2) Locally bypass each IC. Suggested values of 1uF and 0.01uF ceramic caps for each chip should be plenty.

3) Use a fat ground cable back to the power supply.

4) Make sure all logic inputs are driven from a low impedance source (even inputs in unused sections of logic chips). Do not let any logic inputs float.

These are all details that aren't accounted for in many simulations. My first suspicion is that some logic inputs may be floating.

Good luck.

- Lee