I got this weird problem problem with 3G on Xperia Z. On Wi-Fi everything works fine, but ond 3G, only Facebook aplication works, all other apps can't connect to internet. When i share my connection via hotspot, everything loads perfect on other device, so I eliminated sim/operator problem.
Problems started when I upgraded software to 10.5.A.0.230 version, so I tried reset to factory settings but didn't helped, and software version remains the same. I tried all common solutions, like APN settings and similar things, but nothing helped.