Do the Carrots have any Significance?

It is flagrantly, specifically, and entirely a reference to Bugs Bunny. Nevermind the obvious lines in the movie acknowledging this, look at the plot, Paul Giamatti is trying to kill Clive Owen, who constantly thwarts the attempts and comes out unscathed, and humilates him, whereas all of Giamatti's efforts leave him with ruined equipment and dead minions.

All Bugs Bunny cartoons broke down to was someone trying to kill him, and him making a mockery of the whole event. That was it. Nothing deeper. Just like this movie, very "on the surface" about everything.

Owen kept on dropping the lettuce...

"They think I don't know a butload of crap about the Gospel, but I do"!

Carrots help improve vision, which obviously help Smith be such a badass aim.

I don't know, but I'm hungry. Probably Bugs bunny, right?

Carrots having vitamin A and beta-caroetine which are good for eye sight which would be good for the ability to shoot is the significance I suppose

Simply put _+_
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Carrots are good for you; in more ways than one!!!!

its the myth that carrots are good for your eyes so its a way of explaining how good a shot he is.

A widely accepted notion is that Carrots help your eyesight, perhaps this is why he eats them, i'm not saying thats necessarily why, just a suggestion. Not to mention Mr. Smith's remarkable shooting skills, it would make sense for him to do everything in his power to keep a sharp eye.
Those who do not remember the past, are condemned to repeat it...