I applied for a single entry Schengen visa via the Austrian Embassy. They've given me a multiple entry Schengen visa and along with it a leaflet which states to check whether the information is accurate according to the application. There's one point in the leaflet which says to check whether the type of visa (single entry/multiple) is the same as the one you've asked for in the application and to ask for correction if not so. Should I ask for a correction? I'll be in the Schengen area for 15 days and have no plans to leave it until my trip back to my country.
By the Schengen rules, consulates have wide discretion to issue visas with longer validity than was asked for.
It varies between member state and member state (and sometimes between consulate and consulate) how much use they make of this opportunity. Some will issue long multiple-entry visas as soon as they feel convinced that you're obviously not an immigration risk. That way your next application will not clog up their backlogs and they will be able to give better service and still spend the necessary time on applicants with more iffy background. Everybody wins.
The advice in the standard leaflet is mostly aimed at getting you to notice early if by mistake you've been issued a visa that isn't even valid for the visit you applied for. That would need to be corrected ASAP, because it's too late to find out at the border.