Yeah that was an awful episode. Regarding picking up dice, we are lucky that our group is trusty but many of us adhere to the old 40k house rule, that any dice that are picked up are automatically regarded as failures (that practice is especially relevant when you have Imperial Guard or Ork players who can roll over 100 dice, so the ones who are successful are the ones you leave on the table/tray.
I always played 40K picking up fails and leaving hits/wounds/saves on the table to be counted. If a unit got bonus movement that was to be rolled for, it was rolled for in front of that unit and somewhere in the open and wasn't picked up, unless it was in the way of actually moving the unit, until after having moved. All modifiers were announced out loud so that the rolls left on the table made sense to my opponent. If I had equipment or some other mechanism that gave me modifiers then my opponent knew and knew which dice were being affected. It's no less for Infinity. Also, don't have to worry about color coding dice or using different sized dice because there aren't any "mixed rolls", so that's one less complication to have to care about.