I just created a picture for the Miogiro Facebook page, and it took me a lot of trial and error to figure out what works. The profile is that Facebook makes you upload an image that is at least 180 x 180 px, but it then uses ugly JPEG compression on it and creates a smaller, cropped version to accompany newsfeed entries.
Solution? Make your picture 140 x 140 px (Image/Image Size… in Photoshop) and then expand your canvas to 180 pixels (Image/Canvas Size…). Finally, save as a JPEG, not a PNG, with a white background.