Question: What can / should job candidates do to distinguish themselves from their competition?

What should you do?

Ask pertinent questions about the company. If you are applying for a more "strategic role" ask a question about their strategic approach to a certain situation that you have uncovered in your "Research about the company".

Ask the hiring manager about themselves. Usually, I would suggest a segue of "I am an avid learner and hope that my next professional opportunity will help me grow professionally. I am not ignorant to the fact that one of the most important people in my learning/growing process will be my direct boss (hopefully, this is the hiring manager that is interviewing you), please, could you tell me a bit more about you, so that I may better understand who I will be working with?".

Finally, ask for feedback. In the end when they say "do you have any other questions", I would ask "how did I do?" and ask for the job. Yes, that's right. Ask for the job. If you want it, don't be afraid to say "Hi, so, I am really excited about this job. When can I start!!!!". Yes, yes, I know you don't want to sound desperate.

But, you asked "how can i stand out". Well, don't sound desperate, sound excited! You'll be remembered.