1) Long-press "Home" & Power button (opposite of the Screenshot combination)
2) Keep them pressed until the phone shuts itself off
3) Keep them pressed until the phone turns itself back on
That should clear anything stuck in the phone's internal cache.
Hopefully that'll help.
Also, you might want to manually close all the Apps in the Multitasking area once in a while. iOS only actually "keeps" 8 Apps running eventhough all the other App icons remain in that area so clearing them out every now & then should help.