Lt. Columbo deliberately obscures his first name as protection from Death NotesThis ties in with the Death Note theory that Columbo is L's grandfather. The family has known about the Notes for some time, and Columbo hides his first name from everyone in case one comes up.
Lt. Columbo is the mentor to Robert GorenAt some point, Goren studied Columbo's full case history and his methodology, learning as much as he could from them and then adapting them to his own use.
Lt. Columbo is a sociopath.He lies without hesitation in order to catch the culprit. He even fakes feelings. He once faked being in love. His greatest thrill is using the legal system to kill his victims. Yes, some of his victims do get killed — the death penalty was legal in California during most of the original run.
He does not carry the real evidence around with himCome on, this is not a stupid man. It's rather likely that Columbo obtains copies of the evidence to haul around with him. While he has displayed the actual evidence on occasion he's probably not going to put murder bullets in his pocket or into paper bags where they could be lost or tainted. If he really was doing this, almost all of his cases would be thrown out.
Columbo and Quincy are set in the same universeGary Walberg, the actor who played Lt. Monahan in Quincy showed up as an unnamed police sergeant in an early Columbo film Lady In Waiting. Maybe he later got promoted and moved to another precinct?
Coloumbo's wife is smoking hotShe's enough of a looker for Columbo not to chase women who look like Faye Dunnaway.
Grace Wheeler was suffering from ill-effects of her condition when she shot her husbandIt seems her plan to kill him was cooked up on the spot, not premeditated, after he refused to fund her return to the stage. Then not a few minutes after the killing, she promptly forgot about it. Upon discovering the body and through the rest of the episode, she genuinely did not know she had killed the man. Besides memory loss, her condition caused brief psychosis- enough to kill a man out of greed. She certainly didn't seem to be the homicidal type otherwise...
Lt. Columbo is suffering from nightmaresThat's the reason he always appears tired and distracted, especially in later seasons. All the deaths and sometimes grizzly murder scenes he sees keep him restless at night. Also the reason why he keeps himself distracted with trivial things around him, it suppresses the memories.