I play with just Wifi and it works both online and off. My husband has IPad2 also and has Wifi and 3G, the Wifi went down and the 3G kicked in, then a message from GI saying "you have cheated and have used an accelerator, first warning!" The problem, from what we could find out, is that the clock in the IPad can change slightly when the 3G switches on and off. I guess GI needs to hire people to program that are beyond the old 2 cans and a string technology!
I used to love this game, but with the time it takes to visit friends and all the glitches, it is getting old!!