@cicerone imposter,
Of course there are common concepts of "persistent things" due to common perceptual apparatus, language and goals. But notice that we do not USE the word "reality" when engaged with such things
unless there is significant disagreement about states of affairs.
E.g. Some say cycling is healthy, but the REALITY is, cyclists often have accidents.
What the layman does
when asked (by a philosopher) to consider the term "reality" is to assume it refers to what he believes are non-controversial states of affairs despite the fact that he never normally
uses the term "reality" in connection with them. The laymen usually does not understand the significance of
philosophical issues like "meaning is use"(Wittgenstein) or
anthropological issues like different words for "water" according to whether it is culturally taboo to drink it or not. Nor is the laymen likely to appreciate how words can shape thought (Sapir-Whorf) or how it can transmit aspects of social structure through gender norms in lexical selection. All this is implied in Rorty's citation of the term "social construction of reality".
LATER EDIT
Apologies to JLN for repeating some points due to delay in composition.