If you run, say, the telephone wires through the same holes, they'll pick up a maddening 60 Hz hummmmmmmmmmm. You're screwed because when this is discovered, the house is finished, and it gets very very expensive to rewrite it.
The closer the low voltage wires are to the high voltage ones, and the longer the distance, the more hmmmmmmm they'll pick up.
This isn't the main reason running low and high voltage through the same conduit is not code compliant though.
The reason you don't mix low/high in the same raceway is because if exposed low/high voltage conductors come in contact with each other, the low voltage cable has a much higher chance of catching fire.
The closer the low voltage wires are to the high voltage ones, and the longer the distance, the more hmmmmmmm they'll pick up.