Did you put "move armies by clicking" option on?
when moving armies, as aisha mentioned, select move by clicking option. then press and hold on the army at location to confirm the path.
I think we have the same problem on iPad. Probably something to do with the "iApple" browser. So try another web browser.
I have the similar problem on my iOS4s.
I use the move army by clicking option and from what i experienced is that you need to wait for the "screen centering" to occur. I had to tap atleast 3 times before the screen centered to the army before i could continue moving my army and set the army moving.
I'm willing to buy a used iPad/iPhone or other Mac gear to fix this thing, if anyone is willing to sell for cheap.