In Armour of God, when the characters chase a villain to a British-owned restaurant, the maitre d' tries to speak to them in rather dodgy English. Jackie Chan's character angrily tells him to speak Chinese instead.
The 1980s and '90s Godzilla movies feature some of this. In Godzilla vs. Biollante it's used (and mangled) for any time a character is speaking a foreign language (which is disappointing seeing that the previous film featured actors speaking English in American roles and Russian in Soviet roles quite competently). In Godzilla vs. King Ghidorah, as Terasawa is about to detonate a bomb placed on the Futurians' computers, he intones "Make my day!" in a way that sounds half badass, half narm. In Godzilla vs. Mechagodzilla II, during one of the Mechagodzilla training sims, everyone speaks (bad) English. And in Godzilla vs. Space Godzilla, as Shinjo and Sato prepare to give chase to Godzilla on a motorcycle, one of them says "Okay! Aye aye, sir!" with a very thick accent.
The American characters in Godzilla Final Wars (most of whom are Badasses to some degree) never say anything in Japanese. This makes sense for the New Yorkers, and even the two working at Godzilla's Antarctic prison, but you'd think Gordon and Kazama would have taken a "rooma-shi ni toki" attitude by now. But then, everyone understands everything they say anyway, so why bother?
Suicide Club — The psychopath Genesis shouts out "Welcome to my pleasure room!" and sings a song with an English chorus in an otherwise completely-Japanese film.
Nobutada from The Last Samurai likes to say "Jolly Good" around captured American soldier Nathan Algren, at first to mock him for his nationality.
Dostana. There's about as much English in the film as Hindi.
In the 2007 romantic comedy Tokyo Serendipity (original Japanese title: Koisuru Madori), hulking wrestler Satan makes his signature entrance by climbing onto the turnbuckle, glaring menacingly at his opponent, and intoning "GO.... TO.... HELLLLLLLL!!!" in near-perfect English while turning his hand slowly into an ominous thumbs-down.
Theif Catcher, played by Maggie Cheung, says "Good morning" to cops.
Later, when attempting to blow up the Big Bad, she drops a load of dynamite down a manhole while shouting "Happy New Year!" This could be an example of The Cast Show Off since Maggie Cheung spent years in Europe and speaks English fluently.
Another examples occurs when Michelle Yeoh's character learns that her scientist boyfriend is dying. He quietly types "Don't cry" in English on the computer.
This cheesily hilarious Ugandan film trailer has some, especially at the 20 second mark. "YOU AMERICAN SON OF THE BEECH!"
The trailer for the Ugandan action movie, "The Return of Uncle Benon" features a narrator shouting every other word in heavily accented English.
"Non-stop deadly kick-zee!"
"Movie! MOVIE, MOVIE!!! Ugandan movie!"
El Bracero, in Mexican classic movie Ustedes, los Ricos gratuitously and humorously speaks with random English phrases, as he has just come back from living and working in the USA.
Wild Zero has quite a bit of it. The most obvious being the frequent cries of "Lock and loll!".
The Framing Device of Brazilian film Carlota Joaquina: Princesa do Brazil is a Scot telling the story of the Title Character (a Spanish princess that became Queen consort of Portugal - and whose son declared Brazilian independence) to his daughter. Both are Fake Brit (though the father is of English descent), but really convincing ones. And given how decadent Brazilian cinema was - the film marked a rebirth of the country's film industry - you can't blame the producers for using a Culture Chop Suey.
Combined with Lost in Translation: in France, it is common to translate some foreign movies while changing the English title to another title, still in English, but more or less unrelated. For example: