Our 6D was loaned out and when it was returned the person borrowing it told us that the mode dial plate had come off, but...

Thank you both. I saw the Front & Top Cover takeapart guide, but it kind of stopped at the entire top piece and the mode dial is a few steps further. We've taken off the dial plate and examined the inner part more closely. Clearly, the dial took a hit of some kind, depressing 1/3 of the support structures of of the dial mechanism. This is just enough to keep the dial from spinning smoothly and from keeping the center button from being able to push down deeply enough to compensate. Only with a narrow spudger can we push down on the lower dial plate enough to unlock and spin the dial. I've found one source for the dial mechanism, but I'm not comfortable ordering from there, and since there is no further guide, I'm reluctant to take that path also. So, I guess it will have to be a Canon fix. Cheers, Anthony