If you use any of Google's web products, you should be familiar with searching by dates using keys like...
Yes, Picasa naturally organizes photos in date named folders. However, this convenience is lost when importing instant uploads from Google+, which just drops a pile of photos/videos into one "Instant Uploads" folder.
What the Picasa search bar does do is index all text fields/tags in your photos. If EXIF data is saved with your photos, there is a field called "Camera Date" which holds the date (according to the camera) that the photo was taken. This field is formatted as:
(where hours are in 24-hr format)
So, if you want to search for June 2012 photos, type:
into the search bar. So, while this works to grab photos from a specific month, there still isn't a way to find photos from a specific date range. Hopefully, this will be a new feature in an upcoming release.