Big Eater: Nudge. Regularly plundering Martin's fridge.
Birthday Hater: One episode revolves around Betty refusing to reveal the date of her birthday, and even claiming that she doesn't have a birthday. It's eventually explained that she once knew a dying child who wasn't going to live to see his next birthday, so she gave him hers.
Breaking the Fourth Wall: Martin did this during the early episodes, but stopped soon. The entire cast did so at the end of the series finale to take a bow.
Drop-In Character: Had several drop in characters over the years, most famously "Nudge". Inexplicably, one of the drop in characters, Ben, ended up moving into the family proper.
Everybody Dies: The bizarre finale in which the family is taken hostage by a bank robber who blows up their house. The "dad" of the show's title lived on by virtue of having been absent from the show for some time by then.
Royal "We": Nudge used it, when he became convinced that he was long-lost royalty.
Nudge: I'm doing the Royal We here.
Martin: Well, don't do it on the carpet!
Spin-Off: Hampton Court was only linked to its parent show through the Betty character. It was critically panned and cancelled after 13 episodes.
Standardized Sitcom Housing: by contrast, is set in what appears to be a realistic Australian house. Certainly, most Australian houses will have a separate lounge room (or living room) and kitchen, and many lounge rooms will have more than one comfy chair.
Suspiciously Similar Substitute: Continued for a 13th and 14th season after the titular character left, with a family friend serving as an unofficial father figure. Over its long lifespan, the show had a nearly complete changeover of cast, with replacements alternating between thinly-disguised substitutes and unexplained Other Darrins.
Thirty Minutes or It's Free: One episode about a diet, or a hunger strike, or something, that ended with the starving characters giving up and ordering pizza - which then never arrives, because one of the other characters deliberately misdirects the delivery guy in an attempt to get the pizza free.