I have the same problem in iOS 7.0.2, but I'm using an iPad 3.
I'm connected to WiFi and the connection is fine every time.
Exiting all apps
Sending image(s) in different views/screens (photos, shared, and albums: single photo view and thumbnails view) in the Photo app/folder. It just freezes up ('buttons' are greyed out, can't scroll through images, etc..)
Sending smaller (file sizes) images, sending different formats of images (jpg vs. png)
It seems like sometimes it works, but usually it doesn't. Sometimes I have to reboot - and sometimes I've had to reboot more than once to get it to send.
I spoke with Apple Support today. The problem occurs with having bluetooth activated on the device. Disable bluetooth, utilize photostream, then you can re-enable bluetooth.
Tested on both ipad3 and ipad mini retina on ios 7.0.4. Same freezing behavior. Just turn off bluetooth. Will unfreeze photos app and you are able to utilize shared photostreams.
Not limited to type of bluetooth keyboard, speakers, ear piece. It is bluetooth being "ON" on the device.
Apple is aware of the problem (several levels up in the tech dept.) and hasn't found a permanent fix yet. Just use the temp fix above when needed. Keep checking any subsequent IOS versions when released to see if they get a perm fix.
This problem still exists. I have an iPad Air running iOS 8.1.2 and the new (2014) Logitech Type+ case. Photos app works fine, until I try to create a new iCloud Shared Album, then Photos app freezes. I have to force quit it, but the next time I try, same thing happens. I did a reset of iPad and it seemed to work after it rebooted (it let me create a shared album name this time), but it quickly froze again during the process of adding photos to the album.
I disconnected my Logitech keyboard and Photos app immediately unfroze.