I am having the same issues.
1. No WiFi connection from previously reliable at-home routers. The S3 sees the routers and says it is connecting, but then message is displayed "WiFi [or router] turned off." But that is untrue: my iPhone and laptop can still connect to the router without problems. Router is on.
S3 phone can connect to public Wifi at cafes, but it disconnects quickly. This may be due to the number of devices on the Wifi, but I am unsure.
4G data usage is way, way up and I wish it weren't. Would love to get back to "free" WiFi data access. Without WiFi I will use other devices to connect to the Internet and will use my S3 less and less frequently.
Very disappointing.
2. Camera stopped working just after the update. I fully charged the S3, and rebooted, and now it seems to work fine. Spouse may have performed some "magic touch" combination - not really, but when spouse touched my phone, the camera started to work as if there were no problems.
2a. Some photos from the camera were unable to be downloaded into iPhoto on Mac. This problem was never seen before. Message from iPhoto says images are in "invalid format", and lists the images with filenames and a .jpg suffix. My workaround is to email the images to myself and download them to my laptop, then import into iPhoto. Workaround solves the problem, but it's frustrating to have to take several steps instead of just one step.