Flashcards work for a while then stop. Why?
Isolated words decay because nothing retrieves them. Cards with a sentence you actually encountered survive, because the context provides the hook. The rule of thumb is to add nothing you have not met in the wild.
How do I explain recursion without factorials?
Use a task that is obviously self-similar in the physical world: looking for a key in nested boxes. Open a box; if it holds a key you are done, if it holds boxes you repeat the same instruction on each. The base case becomes obvious because an empty box is obvious.
What is the most common way people get this wrong?
Doing it once and never verifying. The setup is the visible part, so it gets attention, and the check that would catch a silent failure never gets written.