Mark -- basically, you're correct. Using the -шь form of the verb without the actual preposition ты can express a hypothetical person -- the grammatical equivalent of using "one" as the subject in English: "One should be careful when one crosses the street".

However, the Russian phrase that you gave sounds more colloquial than my English translation using "one", which to a native English speaker obviously seems a bit stuffy and Jeeves-ish.

In other words, Когда переходишь улицу, надо быть осторожно is a relatively informal construction, but you don't have to worry that it sounds excessively familiar.