At the end of "Bye Bye Sky High..." Columbo is talking about when he joined the force, he knew alot of the detectives were smarter than him so he figured if he worked harder... yada, yada, yada..."And kept my EYE open" maybe I could get ahead...yada, yada.
Any time I have heard anyone use that particular phrase they always said eyes (plural) so it sounded a bit odd to me. I never heard any reference in any episode to the Lt. only having one eye. Do you think that could have been a slip by Peter Falk, or maybe a little joke? Maybe they were just trying to match the character to the actor.
I don't kfl, I think it's pretty common to use the phrase 'keeping an eye open' or 'keeping an eye on' to indicate a slightly attenuated degree of attention to a subject or object. Using the phrase 'keeping my eyes (on, open)...' would indicate a more single-minded and complete attention.
This may just be rumor or Hollywood lore, but I'm pretty sure I remember somthing about Peter only having one eye. If I'm not mistaken, his right eye was removed at a very early age. I assume Peter has made this part of his character.
(Wow! Two posts in one day! I don't usually post this much in a year!)