Never had an iussue at any Disney propoerty, but have had issues at other hotels, even with res in hand!
At one hotel in Milwaukee, was told in very unfriendly manner that we had no reservations (had made through Expedia, who was great at getting us another room and who was not at fault at all). Owner of the hotel called me after the debacle and said our res were in the computer (apparently I think the desk staff at the time was dealing with an oversold convention by denying those who weren't there for the convention).
My tips:
1) Call to confirm before arrival. GET A NAME AND NOTE THE TIME. The first questions asked when you say you called are, "When?" and "Who did you talk to?" In the Milwaukee case, I had called, but didn't get the name of the man I spoke with and they claimed they had no men working the day I called!
2) Talk to the Manager on Duty. I was referred to the "Manager," a woman wearing a maid's uniform, only to find later that the Manager on Duty was at the propoerty across the street at the time.
3) Know the lingo. Hotels are often oversold. This means they book more rooms than they have, because they know some won't show. What they are supposed to do in this case is "walk" customers - get them a room at another hotel. The hotel should be at least as good, and arrangements should be made so you are paying no more than your reserved rate (sometimes even less or free). Also, if the new hotel requires more transportation for you (cab ride there, cab ride to your conference, etc.), that should be payed for as well.
See a similar horror story:
Yours is a Very Bad Hotel