Seems a common issue also with S3's
Try setting the same/different passwords for each band.
Also try forgetting the network each time you change something.
Finally something else I just found to try:
Hey Guys,
Usually "authentication error" error messages refer to a type of second level of security in addition to the pass phrase you've assigned to your wireless router especially if the ‘wireless access point’ is enabled. In this case your galaxy s3 will wifi connect to your computer with the pass phrase but stop short at the wireless access point to return the ‘authentication error’ message.
To fix this, you will need to enter the MAC address of your galaxy s3 in the “wireless station access list”. First go to your galaxy s3 settings page and press ‘about device’, press ‘status’ and scroll half way down and take note of the Wi-Fi MAC address.
Go back to your computer and log back in to the router and navigate to the ‘Wireless Settings” page and click on the ‘Setup Access List’ button. In the ‘Add New Station Manually’ area, enter a device name, enter the Wi-FI MAC address without the semi colons and click ‘Add’. Your Galaxy s3 device is now listed in the table of ‘Trusted Wireless Stations’. Ensure that the check box for ‘Turn Access Control On’ is checked. Click ‘Apply’ and log out.
As I use a netgear router, the wireless settings pages may be slightly different but the words should be similar.
The ‘authentication error’ message should not appear again.
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