These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Ensemble Darkhorse: Joel was a fairly undeveloped character who seemed to just play the role of a PETA lackey. King, on the other hand, quickly gained a disproportionate number of fans. Part of that might come from his being absolutely adorable. The author has taken note of this; when he allowed members of the comic's forum to vote on the plot for the next major story arc following "Imaginate, Too!", he specifically excluded King from the running because he knew everyone would vote for him, and a future King arc was already forthcoming.
Ho Yay Shipping: Again, King and Fox, although King's hitting on the women when he was drunk, in the Universes and Unrealities arc, can be used throw some doubt on his romantic interests. King falling in love with and getting engaged to Fox's cousin Bailey pretty much killed any canon basis for this. Probably won't stop the fanfic writers, though.
A number of commenters on this strip think that a many-tailed kitsune showing up means Rick has watched too much Naruto. Never mind, of course, that kitsunes show up in a lot of old Japanese folklore...
"Hi! I'm Daisy!" Was not originally from Housepets, as some seem to believe.
Just one example: The Alt Text for this comic reads: "This is what YOU wanted. You dirty, dirty people."* The previous comic had a commenter say he should "take a loooong cold bath in the nearest pond" in reaction to the barn cats' offer of a slow-motion pillow fight.
Squick: King is a frequent target of shipping—usually with Sashaor Fox—and King himself gradually gets used to being a dog as the comic goes on. However, some fans still can't look away from the fact that King is not a dog, but a human trapped in a dog's body. It makes his eventual marriage with Bailey still too weird to accept for some.
If you actually start to think about the society that must exist around Babylon Gardens, you can't go far without realizing something disturbing.
Viewer Gender Confusion: Generally, the only way to tell if a character is female is if she has eyelashes. And there are some that don't even have those, like Grape, who is more a tomboy. Even then, some readers get confused. (see: Cerberus) It's gotten to the point that, in his latest style shift, Rick Griffin has started subtlely giving females more feminine features.
All pets who are mistreated in this comic count as such, but King's shaping up to be the top dog for this trope. However, Sasha at Christmas is definitely a close second. Made worse when seen against the other Christmases.
Res is starting to seem this way, though owner mistreatment was quickly quashed as a possible reason.