Christopher,
You are right. It's not working. I don't know if it is the site, or Safari that is to blame.
I can tell you that this site does not integrate with iPhoto. You will find it very hard to navigate your iPhoto Library folder in the finder to find the photos you want to upload. You would have to share>export the images to a new folder on your desktop and then upload from that folder. Not a good and easy way to upload.
May I suggest you sign up for a different Online photo gallery site that is better integrated with iPhoto.
Shutterfly has an Smart upload program that you can download. You then drag images from the iPhoto Library into the top window of the smart upload program to upload them.
Flickr has an iPhoto plugin in that works directly with iPhoto.
ClubPhoto has a program available called PictureSync.app (it is actually not affiliated with clubPhoto but works with clubPhoto and other photo sites.You select all the images in iPhoto and run the software.
Good luck and sorry I couldn't help you with Snapfish. You might want to email them and tell them the problem.
You can use PictureSync to directly upload selected images in iPhoto to Flickr, Fotki, Zoto, SmugMug, Vimeo, You Tube, Photobucket, Webshots, 23, Buzznet, Club Photo, Textamerica, Foto Time and Real PhotoVideo.
PictureSync