Okay, forget about the comic itself (I don’t get it, and besides, this is a grammar blog, not a comic blog).
First mistake; third panel: If you’re talking about distance, use “farther,” not “further.” “Further” is for abstract things that can’t be described by distance.
Second mistake; last panel: He’s talking about the manner in which something is being done, so he needs an adverb, not an adjective. He should say “quickly.”
Third item, not a mistake, but most people get it wrong: His “I” is correct. “I” is the subject of the implied sentence “I can look it up.” People get this wrong so often that you would be ahead to supply the missing verb: “…as quickly as I can.”