I posted something in another S3 wifi thread, but thought I'd post here too.
My husband and I just received our 32GB s3's this weekend. My wifi has no issues. His is doing the same things as described above. We did follow the steps for the *#0011# and that works temporarily but is not a permanent fix.
Because my s3 is working fine, we know it's NOT the router.
Has anyone come up with any other ideas? We'll be calling Verizon tonight.