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Most annoying thing
By far the most annoying thing about Clash of Clans is how easy it is to unintentionally pick up a piece of wall or building or army camp and move it around when you are just trying to scroll around your base. This could be fixed with one very easy feature. There should be a "Lock" which you can turn on or off. When it is locked, you can't move things around in your village. When it is unlocked, it works exactly as it does now.
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While this doesn't happen to me all that much, it would still be a nice thing to have. It would also be nice if it could lock your buildings from being upgraded. If you do try to upgrade something but you forget that your base is locked then "Your base is locked!" should come up in red like when you try to buy something that you can't at your town hall level.