I'd like to share my wi fi dropping issue on my Note 2.
Mine is Galaxy Note 2 i317 with Jelly Bean 4.1.1. I did have wi fi dropping similar issue. I took two smart phones to Target, one is ICS 4.0.3 and the Note 2 is 4.1.1.
The 4.0.3 never has any issues with wi fi connection. But the Note 2 keeps on dropping the connection. I ran an application wifi analyzer to check the available networks. It turns out that Target has so many routers that are using the same ssid, i.e. "Target Guest Wi-Fi". There are channel 1, 6, 11, 2 Ghz channels, etc, as well as many 5GHzs. I did an alias for every available connection. Then I pick one of the stronger signal strength 5G and connected to it.
After that no connection was dropped.
The point is that you should try to connect to the strongest signal SSID so that the Note 2 won't keep on dropping the weak connection.
I have no idea why the ICS 4.0.3 can handle better than the 4.1.1 Jelly Bean as far as wifi is concerned.
But I do notice that on ICS it only shows 2.4 GHz channels. The Jelly Bean shows both.