The (minimal) plot involves a well-meaning but hapless Indian actor who is unintentionally invited to a lavish Hollywood party, causing havoc.
Hrundi V. Bakshi (Peter Sellers) is a seemingly nameless and faceless actor from India brought to Hollywood for a role in a film similar to Gunga Din. Overeager and clumsy, he greatly hampers the shooting until, in a last foul-up, he manages to blow up the set (rigged up with explosives for the great scene of the fort's destruction ... as a loose-laced Bakshi finds a place to tighten his shoe) before the cameras are even rolling, ruining the entire film. The director (Herbert Ellis) is beside himself, fires Bakshi immediately and wants him blacklisted. However, instead of being blacklisted, Bakshi's name is accidentally written on the guest list of the studio boss' party.
Upon arrival, he loses his shoe in the stream that flows through the house and spends a significant amount of time attempting to retrieve it (a scene copied by Amitabh Bachchan in the movie Namak Halaal). As he attempts to engage in banter, guests and host look on in puzzled confusion. The only ones at the party to pay him much notice, at first, are Michèle Monet (Claudine Longet), an aspiring actress who appears to take a slight fancy to him. He later finds a macaw and throws 'Birdie Num Nums' (bird food) at him, which angers the bird and annoys a nearby couple. He also makes a positive acquaintance with a Texan actor who is delighted at Bakshi's ethnic status as an east Indian.
Invitees and attendants include a drunken female guest, an increasingly drunken waiter, his irritated superior, politicians, various Hollywood luminaries, and a Russian ballet troupe that arrives towards the end of the party.
At the dinner table, the drunken waiter (Steven Franken) serves Caesar salad using his bare hand instead of a utensil. During the main course, Bakshi's roast cornish game hen accidentally catapults off his fork and becomes impaled on a guest's tiara. He asks the waiter to retrieve his meal. The clumsy man complies, unaware that the woman's wig has come off along with her tiara, as she obliviously engages in conversation.
Bakshi leaves havoc (and damaged appliances) wherever he wanders. At one point he sticks his hand into a bowl of crushed ice that holds caviar. He then shakes hands with other guests, passing around the fishy odour.
Other obstacles include a control panel with various switches that activate the intercom, the slide-out bar (which Bakshi closes while the bartender is still busy mixing drinks), various retractable floor panels that extend the size of the indoor-outdoor swimming pool, artwork, a backed-up toilet with bidet, and an electric toilet paper roll. This last culminates when Bakshi falls into the pool, to be saved by Michèle. The two bond as Bakshi helps her recover from her agent's unwanted advances and subsequent harsh words.
The would-be hippie children of the executives eventually turn up with a baby elephant covered in stereotypical 1960s slogans.
The action moves to the pool, where Bakshi asks that the elephant be restored to a more dignified state. The entire house is soon overrun with soap bubbles as they scrub graffiti off the animal. The party goes on until the next morning, when the police arrive.
Bakshi drives Michèle home (in his Morgan three-wheeler car) and they arrange to meet again the next week, hinting at possible romantic feelings between the two.