I never found it funny that Data wanted Worf to take care of the cat. Data doesn't respect his own cat enough to be sure if it's male or female, he doesn't consider his cat sentient (any true cat parent will tell you otherwise), and Worf hates cats. So how was that anything funny?
The absurdity of it all was funny, at least for me. Then there are bits like a scratched up Riker handing the feeding duties to Beverly and telling her she'll need a phaser.