I was trolling thru the help screens on the Skinny site and came across this bit relating to APNs on SGS3
"You will now see a screen with ‘Edit access point’ at the top. Now we need to edit the values to the correct Skinny settings. Unless specified below, leave other fields as ‘not set’ (blank) or with the existing values from Telecom XT, they don’t need changing!
• Change name to Skinny
• Change APN to wapaccess.co.nz (do not include the http:// prefix)
• Change MMSC to http://mms.mmsaccess.co.nz
That’s it - all done. We suggest at this point that, just because, you switch your phone off and turn it on again."
That tells me you have MMS working??
http://support.skinny.co.nz/app/answers/detail/a_id/333/related/1