The hypocritical, Cliff Richard-loving lefty activist who was convinced that he was a Marxist rebel, a poetic genius, the voice of an entire generation and the most well-liked and attractive member of the household; he was spectacularly wrong on all counts.
Attention Whore: Oh yes. Almost everything he says is just to get people to pay attention to him.
Bad Dreams: Subverted; He's actually having a rather pervy dream after he thinks he's killed Neil, only for his conscious to wake him up and scold him, reminding him he's supposed to be "Wracked with wemorse."
Blatant Lies: He insists a dress Neil finds in his wardrobe isn't his, despite it being in his size and having his name on it.
The psychotic but strangely child-like punk who couldn't go an entire episode without destroying something — or, usually, several somethings.
Absurdly Youthful Mother: Vyvyan has one, whom we also meet in "Boring". The actress, Pauline Melville, is only nine years older than Adrian Edmondson.
All Men Are Perverts: Spends the entire time when Helen Mucus is in the house staring at her chest (very obviously and even moving his chair closer), happily volunteers to wear tights a girl might have worn, briefly checks out Amazulu when they perform in the house during "Time", tricks the washing machine into opening its hatch by claiming to have Felicity Kendall's underwear, etc.
Ax-Crazy: One of the most violent characters in a Britcom ever - played entirely for laughs. Vyvyan is perhaps the closest live action TV has ever come to a Warner Bros. animated character.
Hidden Depths: Some episodes imply Vyvyan isn't quite as stupid as he pretends to be; He starts accurately describing how the human body produces vomit in "Time", tricks the vampire into revealing it's a vampire in "Nasty" and his potion to turn Balowski into an axe-wielding maniac did actually work. When he actually does go to uni, he's a medical student.
Super Strength: Can kick a sink over, push the entire house forwards, bite through brick, lift Neil over his head, survive being decapitated...
Tsundere: Surprisingly, but Vyvyan has the most friends out of the group, as seen in "Interesting", but Vyvyan claims he "doesn't like any of them." He's also like this towards SPG; SPG is as much on the receiving end of Vyvyan's violence as Rick or Neil, (although SPG usually provokes him) but Vyvyan still cries when SPG dies.
Neil (Nigel Planer):
The whining, put-upon and suicidal hippy who acted as the dogsbody for the entire house and is convinced (accurately) that no one likes him and everyone is out to get him.
Berserk Button: He very nearly hits Rick with a frying pan for mocking his flares.