Can someone recover details from a face blurred with Picasa before uploading to Facebook?

Possibly, at least to some extent. Software blur is not guaranteed to be irreversible: techniques such as deconvolution can sometimes recover detail or improve recognizability, especially if the blur is mild. Some blur-like effects, mosaics, and distortions can be surprisingly reversible.

If your goal is privacy or security, do not rely on blur alone unless it is extremely destructive. The safer approach is to remove the information entirely — for example, cover the face with a solid shape/color, or crop it out. That way there is no underlying detail left to reconstruct.

If the blur is heavy enough, recovery may be impractical, but it’s hard to know exactly how much is “safe.” For anything sensitive, assume a downloaded copy could be analyzed and use a solid mask instead.