By "Arduino ground", are you using an actual Arduino board, or making your own PCB? If you're doing your own PCB, don't run from IC to IC, use planes instead.
Biggest thing is to use 100nF caps on each power pin to ground. Use a 10uF cap nearby each "group" of ICs to remove any power dips. If you're making your own board, a 100uF cap at the PSU entry helps too. If noise is still a problem, you may need to use inductors between noisy components.