A Hungarian woman living in Finland once said to me there were some funny situations when she had just moved here and spoke Hungarian with her husband in public. There seems to be an often repeated, totally innocent Hungarian word that sounds exactly like the Finnish vulgar word for human bottom.
On the other hand the Finnish word kone, "machine", is a very rude word in Italian, or so I've heard. The Finnish elevator company KONE had to develope another name for operating on the Italian market.
Between Finnish and Estonian there are a lot of false friend words since the languages are really near relatives but have borrowed words from different directions. One example I learned at university (and which therefore is probably more trustwothy than the myriad of made up ones I know) is that when an Estonian says he is going to "koristaa ruumiid" he means he's going to tidy up the rooms. However in Finnish "koristaa" means "to decorate" and "ruumiit" (which is how the Estonian "ruumiid" sounds to Finnish ears) means "corpses", so a misunderstanding is almost unavoidable.
Funnily enough there are quite many false friends between Finnish and Japanese too. Some examples are "hana" which in Japanese means a flower but in Finnish a faucet, "kita", Japanese north, Finnish maw, and "kasa", Japanese umbrella, Finnish pile.