Since Android 4.3 update, on Version Samsung Note 2 I continued to get WiFi connection error "Unstable WiFi connection". Also, WiFi internet speed was noticebly low.
I cleared dilvik cache, rebooted, disconnected and reconfigured WiFi - none of which helped. In fact, the problem is not with the phone or operating system. The problem was in my the WiFi network channel. My Motorola router had automatically used channel 1 which was also used by another 4 networks in the the neighborhood.
Install WiFi Analyzer on your phone. Find out a channel with the least interference.
Reconfigure your WiFi network to use that channel. I have had no WiFi errors since then.