Complete Monster: Sister Thornley, by far the most evil character in the series, is responsible for many of the Dude, Not Funny moments involving Otto.
Dude, Not Funny: Child endangerment is treated in a jarringly cavalier manner throughout the series (even more jarringly cavalier than in such "adult" cartoons as Family Guy, South Park, or The Simpsons — both before and after those shows grew their beards and Jumped the Shark): "Hate and Let Hate" is the most flagrant instance, with "Orphan Substitute" coming in a close second, and "The Clownfather" and "Father Figure of Our Country" tying for third, but Otto is involved in hazardous and/or life-threatening situations in several other episodes besides those.
Edgar Allen Poe's misanthropic rampage and subsequent meltdown into the morose author he's known as in literary history as seen in "Every Poe Has a Silver Lining" is not an exaggeration; it is a textbook example of what a manic-depressive temper tantrum looks like. Also worth nothing that the real Edgar Allan Poe was, most likely, bipolar.
Some of the abuse Larry takes (particularly Tuddrussel verbally berating him for his effeminate interests and mannerisms) could be seen as homophobic — if one were to read into it as deeply as they do the Belligerent Sexual Tension between Larry and Tuddrussel.
Freud Was Right: A subversion. Even though Freud appeared twice in the series, all the suggestive imagery involved Larry 90% of the time. Check out the long list on the actual page.
Interestingly, in "Day of the Larrys", the body portrait painting of Larry in blue Renaissance-style clothing is a Larry-fied replica of a famous painting, The Blue Boy. Even more interestingly, Blue Boy is also the name of a well-known naughty magazine targeted at homosexual men (as mentioned in the Cyndi Lauper song, "She Bop"). It also doesn't help that someone (possibly Tuddrussel) wrote the words, "Weenie Boy" on the picture.
It's no wonder too that Tuddrussel had those words written. There's some serious Freudan imagery going on there. That circle that Tuddrussel drew by the side of Larry's face is meant to be a testicle, essentially rendering Larry's head to resemble an erect penis. (Even more so)
Genius Bonus: In "Love at First Flight", Otto asks Larry and Tuddrussel, "In what year was the Magna Carta written?" Larry answers randomly yet confidently: "1895" (the correct answer for the Magna Carta is 1215). "Why would Larry pick that year?" you might ask. 1895 is the year that English writer, Oscar Wilde, was convicted and put on three trials for homosexuality that spring.
In "Ivan The Untrainable," Otto asks Larry if he would like to play with his American Founding Fathers action figures with him. He then says that he could be Francis Lightfoot Lee, who is depicted as a toy in a powdered wig, with makeup, and with rather feminine looking hand gestures. Francis Lightfoot Lee was a signer of the Declaration of Independence, and reportedly a closeted homosexual.
Periphery Demographic: There's a fine line between having jokes for both kids and adults and playing out like something that would air in the early days of Cartoon Network's Adult Swim line-up. This show teeters on it like a pinwheeling tight-rope walker (though you do have episodes like "Day of the Larrys" and "Ex Marks the Spot" where it seems like the tight-rope walker slipped and is clinging for dear life by his fingers).
Plot What Plot: "Day of the Larrys" and "Ex Marks the Spot" seem to exist just so Dave Wasson and his animation crew can piss off the censors with as much Ho Yay as possible and remove the pesky "ambiguous" from Larry's "Ambiguously Gay" description (Not That There's Anything Wrong with That). "Ex Marks The Spot" at least had a historical mission (no matter how thin and easily-resolved it was) to pad things out; "Day of the Larrys"...didn't.
The Scrappy: Otto, in the opinions of some viewers. (It's the voice.)
Unfortunate Character Design: A deliberate example on Larry's case, with hour glass figure and head in the shape of a penis.