When examined by certain characters, such as Wilson, the character will say, "Now I shall eat for a day." This is a reference to the proverbial saying, "If you give a man a fish, he'll eat for a day. Teach him to fish, and he'll eat for a lifetime."
When Fish is on the ground, it flops around, then perishes, its eyes becoming crossed out.
Wickerbottom's favorite food is Fish, judging by her examination quotes. This is referring to fish being considered a "brain food".