As an potential employee: what are the most important questions to ask when interviewing for a Startup?

I've work in my fair share of startups, and even today I feel like on every new one I still miss some important questions on the interview process:

• Financial: What is the burn rate, runway as the company stands today ?
• Who are the investors / Board members, how long have they been, industry experience and connections to the company.
• Vision for the product, proposed path to get there
• Founder's experience

As an early member of a startup I know I'll be actually helping and leading the resolution of some of the questions, but it's important to see where the company, founders and early members stand before jumping in.

What are other questions you have asked and consider critical or important ?

I think that the issues you raise are a good start. Here are five more bullets to add to your list:

• What are your biggest problems? This is a sanity check. If the person is delusional, he will say something like "nothing". If you get the standard answer of "growing fast enough", just smile politely. The correct answer is probably something like "everything".
• What is the revenue? And what are the sources? One customer? Multiple customers? Is the revenue from the product that they intend to sell long-term? Or is the current revenue from something else that is being used to fund the long-term vision? What are the revenue projections going forward? Then the follow on question is, "How will you market and sell to meet those projections?"
• What is the current valuation of the company? If there has already been money invested in the company, you want to ask about the valuation AFTER the investment. Try to think through whether this valuation would make sense for future investors based on the current revenue. In other words, if you are only making $100,000, but you are claiming that you are worth $20MM, you probably can't get another round of funding without screwing your previous investors in the process.
• Who are your competitors and what is your differentiator? There are a lot of ways to ask this question. You could also ask, "What is your distinctive competency?" (If your a Pragmatic Marketing fan.) Basically, you want to know why this company is different from its competitors.
• What is the background of the rest of the team and what skills are you still missing? Does the team have the right skills to actually bring the product to market (design, develop, ship, support, etc) and do they have experience actually doing this somewhere else previously?

First thing: Really understand what the product/service they're building is and ask yourself "do I believe this will succeed? "

If not, leave.

If you do believe in it, then the question becomes "do they have the people/resources to enable it to succeed? "

If both answers are positive, then the only one left is "will this be fun? "

There are three important things that a startup needs to get right:

Technology, Team and Market

If you don't believe in all three, then it's not going anywhere. Ask detailed questions about all three until you are satisfied.

Another good question is "What keeps you up at night?" If they say nothing or give you a BS answer, then maybe they have not thought through their issues. If they have a litany, then maybe they just can't roll with the zigs and zags that a startup will go through.

Great answers here! More:

• Do you get to continue to see updates to the books? (Small startups are risky so everyone deserves to see where things stand.)
• How do you know when something you're doing is failing?
• What are your goals for the company (no wrong answer in absolute sense, but if their goals are not the same as yours, that's a problem)
• (meta) Make sure their interview process is tough, else they're not hiring top people.

Nobody mentioned "pending lawsuits" question.
It's probably not the most important question to ask in general, but it happened in every startup I worked for.
Lawsuits and litigations drain huge sums of money, and have a real potential to destroy the company, especially a cash-strapped startup.

Aside from all the ones given, I actually need to know if they plan on staying in the same geographical location for long, this has been a strange recurring issue.

Lighter questions

• Do you have a solution for coffee?
• Do I have a budget for a computer, or someone's left overs?