-Their marriage response is random, not relationship level-based.
-They are unaffected by ghosts.
-They can talk to themselves to alleviate loneliness and stress.
-When painting stylized still-life, they can create distorted paintings.
-They can autonomously sit in bathtubs and/or on toilets without using them.
-The "Speak Madness" social interaction will creep-out non-insane Sims but will entertain other Sims with the insane trait, and give out a bonus in relationship the first time if the Sims have not found each other's insane Trait (and mark it as discovered). It takes a very high relationship at best friend level to get a sane Sim to react positively to the said interaction.
-They can fish in swimming pools, which childish Sims can also do.
-They are prone to random mean interactions for little reason. This can be countered if they have the friendly trait.
-They will (also autonomously) consume fruits from their inventory, even when they're not hungry. This can result in them getting the Stuffed moodlet.
-They will always wear sleepwear when travelling to a destination world. (World Adventures)
-They will cheer for the Emperor of Evil, unless they have the Good trait as well.
-If they suffer a romantic betrayal or break up, they may end up taking out their frustration on another Sim at random instead of their cheating/former romantic interest.
-They strangely never autonomously use fight interactions, even if they are mean spirited, evil or hot-headed. They may still slap Sims for a dare if they use the "Watch This!" interaction from the daredevil trait. They may also start using fight interactions if they have suffered a romantic betrayal or break up.
-Their wishes may not always make sense, and can be granted wishes that aren't for their trait and/or life state. For example, they might want to steal an item, while they lack the Kleptomaniac trait.
-They are prone to causing inappropriate behavior when visiting another Sim autonomously, giving the host the Rude Guest moodlet, which can be countered if the said insane Sim has the Inappropriate trait.
-They will randomly get the wish simply to leave the house.
-They will sometimes act like one of the major pets you can create in Create-A-Sim. (Pets)
-Interestingly, the Talk About Conspiracies interaction will be considered friendly, and it will usually be received positively. On a side note, the "Catch Anything?" interaction will allow the Sim to discover if the target Sim has the angler trait, and if so, give a bonus to the relationship.
-They can refuse to follow the Sims 3 Dress Code by exercising in any of their outfits instead of the required Athletic, going to work in a similar manner, and if they have the Never Nude trait, they will shower and/or take a bath in any of their outfits.
-They act nervously when swimming like a Hydrophobic Sim, but will not suffer the ill effects of doing so.
-Oddly, they will still get the Lunacy moodlet on the night of a full moon. (Supernatural)
-They will randomly cast Ice Blast on plumbing objects, which breaks them in the process. (Supernatural, witches only)
-They tend to perform their "catch and eat invisible fly" animation when something unfortunate occurs to a nearby Sim.
-Like Neurotic Sims, they can autonomously look out a window to slightly boost their fun.
-Regardless of their mood, they may have a warped expression.