Oh yeah Bring in the son, have him be a chip off the old block but in the now.I think it'd be fun(if the show or pilot ever gets made),to have the son call the father every now and then for advice but you never see him,(kinda like the original Columbo's wife), but he's not a slouch.He can break bad, and run the bad guy down if he has to.His weapons would be his mind of course, and ... just toying around.... a Jeet kun do expert?Might be a bad Idea I don't know. Of course most,save the police department,would under estimate him to begin with.That was one of the fun things about Columbo Sr.
So yeah frumpy,disarmingly simple/clever, and a bad ass. Have him put naughty CEO's and Politicians in jail. I would have to say though that no one can take Peter Faulk's place.The son would have to have his own quirks.