Hi Fred!
I am sure I know #'s 1, 2 & 3, but as I always say, I won't be a quiz piggie, so I'll only answer one of them.
#3 is from Death Lends a Hand and Columbo says this to Brimmer about his shag rug at his beach house. It is where Brimmer is searching for the "missing" contact lens.
This is one of my all time favourite lines when Columbo says that he bets you could lose a shoe in there for a week!!

I'll take number 2--By Dawn's Early Light.

I'll hazard a guess at number 4 although I'm not entirely certain - was this said by Columbo in Columbo goes to College when he is talking to the Law students?

Yep, you've got it right :)

OK - is number 1 Requiem for a Falling Star? I reckon that makes sense. And I'm sure 2&4 are right but haven't a clue about 3 - will trust all of your superior Columbo knowledge!

Everyone beat me to it. You will just have to trust the fact that I already knew the answers to all four questions -- including the survival of the ploy to make the incorrect guess of "Agenda For Murder" for number 4.

David of course I believe that you knew all the answers! You always do!