I agree with you wholeheartedly about "could care less."
However, as a British person I see a rather useful distinction between "while" and "whilst." In British English, "while" is commonly used to convey the idea of "at the same time." On the other hand, "whilst" is commonly used to convey the idea of "although."
For example, consider the sentence "John is often lazy while his wife works hard." And, on the other hand, "John is often lazy whilst his wife works hard."
In British English the first sentence might well be construed to mean that John's laziness comes upon him especially during those times when his wife is hard at work. Whereas the second sentence conveys the idea that John is in general a rather lazy person, but his wife is in general a hard-working person.
The example is not ideal, and one could maybe debate the question of whether the "while" or "whilst" should be preceded by a comma. One could probably construct a better example. But the general distinction of "while" meaning "at the same time," and "whilst" meaning "although," can be quite a useful one.