Look. If you've been a professor, you don't even blink at this scene. It seems, based on the time of year, like this is at the beginning of the semester, although oddly some of the student requests seem like end of term things (like the paper).
However, go to a faculty office, of a professor who has office hours and teaches a class with a lot of students (or an advisor and professor, like me). I can't walk the 60 steps from my office to the bathroom without being stopped in a rapid fire of questions: Dr H, did you get my email? Can you add me to that class? Did we have homework? Can you tell me where to get my book? Are you sure I can't take that class? Do you know my ID number? (I am not making any of these up). In fact. Dr. Jones' response is the one that many of us wish: that we could just climb out the window and sneak away. Dang it, my office window doesn't open. And seriously, a secretary? Oh, the good old days that none of us can remember, when academic departments had budgets with actual money in them and apparently staff galore (I suspect this is nostalgia re-writing actual history to some extent, but we can dream, can't we?)
This scene is not indicative of Dr. Jones' teaching competence or not, necessarily; it in fact is reasonable that he'd say he could see every student in turn, and equally realistic that he'd despair at getting through the line. Again, I've been putting my key in the door to lock up, hurrying to get to a rehearsal on time, when a student says "I just have a quick question" and it takes five minutes to ask and then there are three other things and oh hang on, let me find my laptop and turn it on and show you...and all the while something inside you is trying to scream...Sorry, was this too emotional? Anyway, that is what it looks like from inside academia.