A few have come to mind... костюм / costume. To us, a costume is a fancy dress for a performance or entertainment. деталь / detail. The English "details" can mean extra information, as in "Ask at reception for details" (My English-speaking colleagues discussed this at work just recently, ie. why use подробности and not детали?) макароны / macaroni. Our macaroni only means the tiny curved tubes of pasta. пакет / packet. To us, a packet is closed and sealed. It's not an open bag. адвокат / advocate. An advocate is a public supporter of someone or something. To use "advocate" in a legal sense is uncommon. совет / Soviet. No meaning of "advice" in the English word... we only think of the USSR. I'm sure someone has made a list somewhere, but these are ones that I've come across personally.

I have been thinking about your question for quite a long time now and I could not come up with any false friends between English and Russian. I have one for Russian / German: Butterbrot. In German, this is a bread with butter (and butter only), while in Russian it is more like a sandwich which can also have cheese, sausage, or whatever on it. Sandwich in German is a belegtes Brot. And I have two for Russian / Serbian: zhivot in Russian means belly, while zhivot in Serbian means life. And ljubit in Russian is love, while in Serbian it means kiss. Maybe one example you can use for English / Russian: arbitration / arbitrazh. While these appear to be cognates (words with the same origin), arbitration in English refers to what is known as treteyskiy sud in Russian (thus a private court), while an arbitrazhniy sud in Russian can be either 1) a state commercial court (khozyastvenniy sud in Belarus), or 2) a treteyskiy sud. There is also a word in English, "arbitrage" (pronounced similar to "arbitrazh" in Russian) which is only used for a certain technique in finance. Arbitrage there means to use different prices for the same thing in order to buy cheap and sell expensive (and make profit). For example: If one dollar buys you let's say 1 rubel in St. Petersburg, but you can sell 1 rubel for 1,20 dollars in Moscow, you buy 100 rubel in St. Petersburg and sell them for 120 dollars directly afterwards in Moscow. That way, you made 20 dollars profit. I hope that this is helpful. Ya podumayu eshche, esli eshche shto-to spomnyu, snova pishu.