Jif in America
Jif in Australia
Also:
Thongs (yes, it IS safe for work, trust me)
Nappy - a noun, not a verb
and the word “momentarily”, which means “for a moment”, not “in a moment”
Oh my god–my favorite Trevor Noah bit involves him getting a taco and a napkin. Watch it!
We actually have the same slang term for the penis in the US. It’s not one I hear used in conversation that often, but I definitely remember there being plenty of jokes and snickering about the title of that movie.
I’m not sure there’s anywhere that this is a false friend. I understand that it’s a diaper in a few other English speaking countries, but in the US at least nappy doesn’t mean anything, as a verb or otherwise.
The flapjack thing gets worse. Last time I was in LA a server heard my accent and was really pleased to say they had “English flapjacks” on sale. They were actually something close to millionaire’s shortbread (no oats met this food) - definitely not a flapjack in England.
Casserole. In the US that’s one of many things. Many, many things. Even a lasagne is a casserole. And you can eat a cold casserole and enjoy it! In the UK it’s a dish that is cooked in the oven, involves multiple ingredients but does not involve layers, involves gravy that is not like any US gravy, and you would only eat it cold if you were literally starving.
Grill. UK - cook something via warming up striated heating elements above it. US = cook something by heating the same kind of elements below it.
Pavement. In the UK that’s a sidewalk, and it’s intended for pedestrians. In the US it’s what in the UK is called tarmac, the material used on most roads. If you’re reading about someone hit by a car while walking on the pavement it’s probably a UK source and it doesn’t mean they were jaywalking.
Vest. British people use the word vest to mean “the thing you wear under your other clothes, for warmth or comfort.” It’s usually sleeveless but can have sleeves, even full-length ones. It’s not what you’d wear in public. You certainly wouldn’t don your smartest vest to wear at a wedding and expect people to compliment you on it.
Jumper, I think, is well-known in the UK as meaning sweater in the US; we often adjust our language to accommodate. What is not widely known in the UK is that jumper in the US means a sort of dungaree dress or a thing worn by babies. I have had actual confusions with US friends who didn’t know what I meant by jumper.
In Australia (and probably UK)
Cot: baby bed. Crib is not a word in use.
Or a valve for his Orange. 
I believe the garment you are describing is known as a jump suit, as in typically worn by aviators or parachutists.
Interesting that the US friends did not recognize the word at all, though (what do American sailors wear? Jerseys?) I suppose they thought it had something to do with electronics?
It’s just occurred to me that the OP’s own name has different meaning in the US. There it’s usually synonymous with “popover” (we don’t use the word popover in the UK) and often involves sugar. A Straight Dope friend of mine asked for Yorkshire Pudding recipes once and I was genuinely baffled. There is one recipe. One. It can be big or small, and you can replace meat with not-meat, but you certainly don’t add sugar. Also you don’t eat them cold.
It’s not helped by sites like this saying that Yorkshire Pudding is a savory dish that uses popovers, and covers them in gravy.
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. It’s not a dish. The poster Yorkshire Pudding may be a dish for all I know (flutters eyelashes :D) but it’s an element of a dish, and you can have it without gravy, and certainly not with American gravy; having the larger version with gravy as a starter makes it a dish, but on its own it’s not. It’s like saying roast potatoes are a dish.
Crib is a specific type of baby bed, a small one that is often on rockers. In the UK anyway. I think the US uses that word for both a UK crib and UK cot.
The US cot doesn’t really have a word in the UK. Camp bed or something, maybe?
Multiple sitcoms - oh, Brad is staying over, I’ll get the cot out for him. When I was a kid, if Glenn hadn’t been introduced prior to this, I was then confused when he turned out to be an adult. OK, so Glenn’s here now, but where’s his kid? If I already knew he was an adult I just thought American cots were as big as their cars but was confused as to why someone would want their guest to sleep in something with bars and why did they have one hanging around anyway? These are childhood households that have barred baby beds stored for… their guests?
No she was describing an American jumper correctly. It’s a dress, typically worn by toddlers and little girls but not uncommon for grown women too.
I watch a lot of British TV and their use of “jumper” still confuses me all the time. I think it’s more of a crew-neck sweatshirt for us, than a knit sweater, fwiw.
Edited due to intervening posts 
Americans usually wear sweaters, I think, in the same way we wear jumpers. A jumper is a crew-neck sweater and a knit sweater though.
It might have been in the context of me posting a picture of a baby wearing a jumper and hem being confused - I don’t remember and just to be clear I don’t think their usage of the word is wrong, just different.
On the other side in the UK a bib is ONLY a thing a baby wears to protect its clothes from food. In the US it’s the upper part of dungarees or the thing you wear under a formal tuxedo - I think they use bib for the baby thing too, though I stand to be corrected.
Yeah the most common meaning for “bib” here is a baby’s bib. But we also have “bib overalls” which you would call “dungarees.” And non-bib overalls would be a jumpsuit or coveralls 
Nappy means several things in the US. It means lint balls on wool sweaters. It means a bad thing for African American hair. Or taking an afternoon sleep for my kids any way.
It’s in the upper Midwest that I’ve seen the term “hot tamale” applied to sloppy joes. I don’t know how current it is, but my mother-in-laws Wisconsin parish cookbooks from Chippewa Falls all had recipes for “hot tamale” which was a sloppy joe. There was even a thread about it here on the Dope. That thread specifies specifically the Sheboygan area of Wisconsin, but the cookbook I read was from Chippewa Falls. Apparently, some people also call sloppy joes Spanish hamburgers according to that thread.
That thread also has the interesting tidbit about how the word “mango” means “green pepper” in parts of Indiana, Kentucky, and Ohio.
I only very recently found out that a “fancy dress party” in UK English does not denote a party with formal wear, but rather means “costume party.”
Also, in regards to the word “fag,” which I’ve been fairly used to for awhile to mean “cigarette,” I was still taken aback when I heard a British friend of mine say “I could murder a fag,” which means “I really desire a cigarette.”
A different example of false friends: in France, you may be expected to march as part of a manifestation, whereas in English that does not quite work. You could be at a political demonstration, but French demonstrations have more to do with mathematical proofs.
We used “rubbers” in Canada too, at least when I was a child. Never thought of them as erasers; they were simply rubbers. And the teacher didn’t find anything wrong in telling me (for example), “You made a mistake here, rub it out. Oh, you don’t have a rubber? See if you can borrow Johnny’s.”
Growing up in WASP Ohio we often had the ground beef, tomato and macaroni dish but I don’t recall it having any name. Even today I wouldn’t call it goulash. I had some friends who called it slumgullion.
Dennis
I think it’s mostly died out as the availability of the fruit has increased, but in parts of Appalachia and some nearby areas of the Midwest, bell peppers used to be (and occasionally still are) called mangoes.
This threw me the other day, when Americans on reddit were talking about the most rootable Survivor contestant. Domenic? Eww, no. Oh, you mean who are you barracking for.