I have read something about people being able to see private photos on Photobucket through a method called "fusking".
You can read more about that below, and I've also included some videos and links that might be helpful.
Please don't use this information to view private Photobucket albums without consent though, I am only posting this info up as a reference to show how vulnerable accounts on Photobucket are, even when the albums are set to private!
How to see private albums on PhotobucketPhotobucket has a serious privacy problem. I am not a hacker and I have been able to see private albums and photos on photobucket.The thing is, the application handles security differently than other more secure photo sharing services Instagram or Flickr. Instead of allowing the user to handpick the privacy settings for each photo, on Photobucket this is done on an "album level" ( so entire albums will have one of these privacy settings: "Everyone," "Private," or "Password-protected"). You can therefore make albums private in that people searching for them or browsing your profile won't find them.BUT, hackers can still find each photo if they have the direct Photobucket link that goes in the url bar of the browser!
So in theory, once someone has shared a photo on Photobucket, they have compromised the privacy of that photo.
Because all it takes is one person to share that link with someone else, and the private photo can become visible to all that have the url!
And the internet is full of tutorials on how to use this fusking trick to exploit entire albums.
Here's a video tutorial as an example:
Here's a link with even more detail about how to hack Photobucket private albums: http://internet.blurtit.com/3976326/how-to-view-private-photobucket-albums-2014