I recently finished a master's degree in mathematical logic, which is expected to be rigorous. I would say that 80% of the lecture time was pure, unfiltered handwavyness. However, filling gaps and formulating actual rigorous statements was 100% expected of the students. I personally think as far as lectures go, that the higher the math, the more important it is to convey ideas in a fluent, often informal way. Then, if you are mature enough, you will be able to "clean it up" in your study time.
There are however, some who say that lectures are an absolute waste, and you should always skip them and go straight to books/written sources. I don't share this view, but I understand it.