Yes, the public drinking and womanizing would definitely have been picked up by the media - unless the club was so private and the its members were very tight lipped. I don't think there is any club that private.

Or perhaps the writers wanted to paint the commissioner as someone so bold he could not have cared or thinks he is so important that no one would mention his drinking and the media would ignore it if someone did.

Regardless, it seems to me that in all Columbos the writers want to establish something about the murderer victim right away so we are ether sympathetic to them or disgusted by them from the start. In this case they wanted to establish right off that he was not the most admirable person in the world, or just a bit to bold.