Becoming a science professor sorta snuck up on me. Not getting the title, as that happened at a distinct point in time (namely the first of January 2009), but the 'separation' from being a student and then postdoctoral researcher grows somewhat slowly. A colleague of mine recently expressed surprise when he discovered his students were somewhat daunted when speaking with him (this is partly as there is the perennial fear of "looking stupid" that students have), and I'm pretty sure my fellow faculty member does not feel that different to the students he talks to.
The important point, I think, is that students should realise that you don't get smarter with age; in fact, it's probably the opposite. What you do gain is experience. When a professor speaks from authority, it is not necessarily that they are "smart", but they have gathered significant experience over the years. But it's important to realise that there is a limit to experience, and just because a particular professor makes a pronouncement, it doesn't necessarily mean it's correct. Over at Letters to Nature, Luke Barnes has a nice article on appealing to authority.
Anyway, I just wanted to add to this a marvellous quote
In high school, my two idols were Einstein and Feynman. While Einstein felt that QM must be wrong, Feynman felt it was the ultimate truth of the universe. This discrepancy bothered me, and I wasn't sure who to believe. So, about six weeks into physics X, I screwed up my courage and asked Feynman about the "dice" and Einstein. "Dr. Feynman", I asked, "Einstein was one of the greatest geniuses of physics, and certainly a lot smarter than me. He knew more physics that I ever hope to. But, he didn't believe in quantum mechanics--so why should I?"
Feynman paused -- which surprised all of us -- and smiled. He looked at me and said, in that wonderful Far Rockaway accent, "Nature doesn't care how smart you are. You can still be wrong." He went on to explain some background on Einstein's view of physics, and why he might feel that way.
"Nature doesn't care how smart you are"; I think that's an important lesson that all of us should remember.