As mentioned before, close proximity of electrical wires to non-electrical (phone, TV, etc) will likely cause signal problems on the phone/TV wires. For good 'ole fashioned analog TV, you'd likely see static or a herringbone pattern in the signal - for a satellite run, you'd probably see rain fade problems increase.
From a safety perspective, if there's a cut in the electrical wire and in the adjacent coax (yes, it should be fully insulated, but it may have been nicked during installation without your knowledge) you don't want voltage going into the piece of coax that people freely touch knowing that there's never high voltage in coax. Yes, the odds are against it, but if you're unlucky, it's a painful lesson. Many things in the code protect against seemingly impossible circumstances, but most have catastrophic results if Murphy isn't on your side.