I think there is a basis for a 'common' language. There is even a real world equivalent. The term 'lingua Franca' technically has the same meaning as 'common language', though it does specifically refer to French. This is simply because at the time the term was coined, French was a common language.
Now, I'm not saying that everyone would know the common language, and the common language for one area might not be the same for another, but in any area with extensive trade, a single language tends to dominate. An earlier poster mentioned English, but then qualified the remark. That's not necessary. More people speak English than any other language. There aren't as many people with English as their mother/father-tongue, but more people learn English as a second language than any other language in the world. Why? Trade.
It was the same in the Medieval and Renaissance periods of our world. In Europe, educated people spoke Latin, and at different points in history, a merchant would speak French, Italian, Spanish or Dutch. In the Orient, all educated people spoke Mandarin. In fact, the written Chinese language (I call it Hanja, simply because that's what it was called in Korea, where I lived) has the same meaning in Mandarin, Cantonese, Korean and Japanese, though when spoken, the word is in the language of the speaker. Wild, eh?
So, while I completely agree that a single common language, known by every individual the world over is ridiculous, there is precedent for a geographically focussed common language used by the intelligentsia and possibly another for trade. In my world, one section of the setting has a unifying religion, which uses an otherwise dead language (Latin, anyone?), and that language is used by intellectuals, while the language of the regional economic powerhouse is a kind of 'trade common'.
Also, on the topic of adventurers learning many languages, I don't find that too hard to believe. Your average mercenary soldier in the Renaissance could probably speak around three languages well, and would have smatterings of very many others. Of course, the likelihood such a mercenary could read any of these languages was small, but multi-lingual individuals, in certain strata of society, is well within the realm of believability.
Sorry for being so long-winded. Hope this is of interest to someone. Take care.