Hi Kerry,
As an avid flip flop wearer, I totally get your question.
I am happy to report that there aren't any rides or attractions that I can think of at the Walt Disney World Resort which require you to be wearing closed-toed shoes.
I know that when I'm wearing my flip flops, the only time that I have had to remove them is whilst experiencing Soarin' at Epcot. This is because your feet dangle in the air whilst on this attraction. Wearing flip flops is not an issue though as you can simply place them in a little basket underneath your seat whilst you ride.
You will find that there is a dress code which Guests must adhere to at most of the
Fine/Signature Dining experiences at the Walt Disney World Resort.
Where there is a dress code in place, this will be noted on the page relative to each individual restaurant within the Dining section of the Walt Disney World website. For example, if you click on the California Grill
and scroll down the page, you will see that the dress code is noted as detailed below:-
Dress Code At this signature dining experience, Guests are asked to adhere to the dress code.
Men may wear khakis, slacks, jeans or dress shorts and collared shirts. Sport coats are optional.
Women may wear Capri pants, skirts, dresses, jeans or dress shorts.
Not permitted are tank tops, swimsuits, swimsuit cover-ups, hats for gentlemen, cut-offs, torn clothing and t-shirts with offensive language and/or graphics.
As you can see, long pants aren't necessarily required - in this case, dress shorts would be acceptable.
Emma