I'd really like to see this addressed too, for me its the only thing I have a real problem with, the app would be pretty much perfect for myself and my wife if this was fixed. I often accidentally tick items off, often without knowing it has occurred when I'm not looking at the screen, often we haven't fully cleared out the area at the bottom from our previous shop and these items are then quite hard to identify.

Some excellent suggestions above, be great to have the option to pick a preferred method, personally I'm all for click and hold or swipe across, I'd love a settings panel so I can choose the method that works best for me and those that like the status quo can keep it as it is.