Should you get an opportunity to sit down for an interview with a partner in a venture fund,  here is a list of points for any interview  - as they say, Success = Opportunity + A Prepared Mind. 
•    Research the venture firm’s profile. Understand the sector and stage of investments, assets under management and its latest fund size.
•    Look up the key portfolio companies and map their progress. Have these companies signed up strategic partnerships? Have they raised follow-on rounds of capital? How do they compete with others?
•    Research any major exits - it's always good to start with the positive. A congratulatory note on an exit is not pandering - it's just a nice way of showing you have done your homework.
•    Read the founders and senior partners bios, tweets and blogs. Understand their mindset and philosophies well. If they hate Ayn Rand and you like her, well....

Examples of questions you can ask at an interview:

1)   Fund’s investment strategy:

• Of course, you have done your homework, checked out the websites and online data sources. You know the firm’s history, and primarily the background of the founders.
• Research one or two specific investments, and assess the competitive universe of similar investments made by other venture firms. Dive into the investment rationale and find out why this opportunity was chosen over others.  
• Ask how the fund’s investment strategy has evolved over time. What challenges has the fund faced, if any, in sourcing opportunities? In raising capital? 
• Find out the life-cycle of the current fund i.e. recently raised, partly invested with 3 more years to go in the investment cycle. All venture funds have a 3 / 5 year investment period from the time the fund is raised. Thus, depending on the timing of your entry, you could be involved in making investments, managing the portfolio or preparing for the next fund raise.

2)    A typical day at the firm: While this is somewhat of a cliched question, it's a good way to get some insights. Who would I report to and what self-development opportunities exist for an entry-level person? Look for opportunities where you will participate in all facets of the business. 

3)    Chemistry and Culture: This is best found via offline reference checks and informal conversations, especially with portfolio entrepreneurs. Is this a collaborative environment or a field of cowboys who thrive solo? How does the team collaborate with each other, especially when the portfolio companies are in trouble? When has the firm let go of any people and why?

• Look for troubling situations and how were these handled by the internal team – be prepared to get smooth talked. You will rarely hear honest statements like “We screwed up on that investment” or the GP “screams his head off and throws things all around, muttering obscenities”.
• Look for insecurity amongst the existing partners. In one interview on Sand Hill Road, the first thing a candidate was asked was "I don't know what the f___ is going on and why you are here?" Needless to say, the firm and its key people were struggling with infighting, politics and such.  New hires often suffer when they jump into such cesspools. 
• Can you see yourself having fun with this team? A beer on Friday night?

4)    Performance / Rewards: How will my performance be measured? What milestones would established? Will I be able to measure my own progress?  At what point will I be eligible to be on a “partner-track?” Often the position description will state if it’s a partner track position.

Of all of these, in my opinion the culture and chemistry matters most. You want high integrity, a sense of camaraderie and a very high discipline for performance.  Very few firms truly have a healthy mix of all three.