On more than one occasion I have heard expats praise Estonia for its general similarity of attitudes to their home country. I've heard an American housewife say that she could live quite comfortably in Estonia as long as she had access to a Stockmann, and I've heard a British rover say that this is the only country, other than home, where he would consider raising his (hypothetical) children.
Nevertheless, there are a few things foreigners will have trouble with. First and foremost, this would be the language.
Admittedly, most people in Estonia do speak at least some English, but if you're going to stay here for an extended period you will need to start learning Estonian. Be prepared to become the source of much merriment to your local acquaintances in the process.
Most European languages belong to one of two groups, Germanic or Romance. The former notably includes English, German, Dutch, and most Scandinavian languages. The latter includes French, Italian, Spanish, Portuguese, etc. Both of these groups have evolved from a single source, and belong to the Indo-European family. The upshot is that if you are proficient in one of these languages, you will be able to logically deduce similarities in others, at least on the level of word meanings. In almost every European capital, traffic signs pointing to downtown will be some variation of Center.
Not so in Estonian. Along with Finnish (and, inexplicably, Hungarian) it is a Finno-Ugric language, and has nothing to do with the rest of them. Centuries of conquerors have left a mark on the tongue, but it is still beyond the comprehension of anyone who is not born into it. I've been speaking it all my life, and I'm still not entirely comfortable in it.
It's more than just the grammar, which you may largely ignore if your intention is simply to get by at the supermarket. Estonian shares with Irish and Dutch the distinction of having fundamentally counter-intuitive pronunciation. Unlike those, the Estonian language tricks you by being entirely phonetic; you take a word, and you start pronouncing it from the first letter, taking each in turn, until you get to the last one. No skipping, and formally at least, no assimilation. What you see is what you read.
Except that it isn't, because each sound is subtly but importantly different from what you would expect it to be. I've known Finns who have lived in Tartu for years or taken extensive language classes - and they still speak with a bad accent. I cannot possibly describe in words the entertainment value of a Cambridge-educated Brit trying to pronounce the name of the pub Püssirohukelder.
So if you're an expat trying to speak Estonian, remember: your local friends are too polite to laugh in your face, but they are in fact fairly miffed at what you're doing to their language.
Except if you're speaking to South Estonians. In that case, never mind, it's not your fault; nobody really has a clue what the fuck they're on about.