I think it should be clearly stated in the Badges section.
For example, consider Vox Populi bronze badge:
Used the maximum 40 votes in a day.
This says nothing about possibility to get awarded with this badge multiple times. I think that even bronze badges are something of an achievement for new users, and this improvement could make things less confusing.
Am I missing something, or the best way to tell if badge can be gained multiple times is to check profiles of most dedicated users and see if any of them has that particular badge
x3 for example?