After explaining skip-lists and sketching up the Big-O complexities for best and worst case for sorted and unsorted data... the interviewer turned to me and asked why wouldn't I use a skip-list (it should already have rung bells that it wasn't "in which instances might you not use").
My answer was that each problem should be understood in terms of the data and task before choosing a data structure and algorithm. That answer was rejected.
The interviewers answer: "No, you shouldn't use skip lists because the memory of all those extra pointers is too much for the JVM."
The biggest misconception I've come across is that Big-O says anything at all about the language you're coding in and your implementation.
I did point this out, but was shot down pretty fast.
The company in that scenario was AWS, the position was architect level. I didn't take the job. Interestingly they offered me another job different from the one that I had been interviewed devoid of any product dev at all on the basis that I was "too technical" for any role that included product.
Big-O doesn't care for your implementation.