I had some major problems getting my Mobile Hotspot to work. At first it was very difficult to connect to anything and then a few days later it would not connect to anything.
I went to Verizon and they told me to do a hard reset. After I had spent 3-4 hours setting the phone up, this was not a welcome option.
After the Verizon person looked at everything, he discovered that the Hotspot would work if you set it up to only connect with specific devices.
This meant that you had to find and enter the MAC address on the Wi-Fi device that you wanted to connect to.
Since this was a very short list, I went home and tried it and it worked.
Good news! The next day when I was exploring my S3, I discovered that the Hotspot would work on any Wi-Fi as long as you turned all the security "OFF" on the S3 and made it "OPEN" to anyone.
The security aspect of this does not concern me so I am good to go.