1. What's a typical day like for someone in this position?
This is a twist on the standard, "So, what will I be doing?" question. The companies will likely have given you reams of material on what the entry-level program is like. The idea behind this question is to see how the program is structured on a day-to-day basis. You'll learn more about the mix of education and work experience, whether you'll be working on your own or with other new hires, part of a larger team within the company, etc. You're looking for how you'll fit in and what you can expect.
2. What are the opportunities for advancement?
This is a delicate question, since you're looking past this position to, potentially, the next couple. But it shows that you're interested in having a future with this company as well. Hopefully, you'll get a sense of not only what other entry-level hires have gone on to do, but also whether there's a lot of turnover there. Companies that stress patience and a long haul may be very popular places to work, though the flip side is that they could also be stagnant. Likewise, if there's the promise of rapid advancement, are they bleeding people or just growing fast and improving their fortunes? Best to ask follow-ups as much as you can. Find out why things are the way they are.
3. How is compensation structured?
This is a nice way of asking, "How much will I get paid?" without asking. Some companies have gone to a base salary plus bonus system like major Wall Street firms -- especially those employers actually part of a major banking company. Others retain a basic salary format with some kind of performance bonus -- much smaller than those on Wall Street, but the overall salary is bigger. This is also a good opportunity to ask about benefits, though again, be sure you don't ask repetitive questions if the information can be found elsewhere.
4. How does the company handle continuing education?
This is a key question. You still have at least five actuarial exams to go before you become a society associate. Most firms will pay for your exams, but it's good to ask regardless. Some companies offer further training or study assistance as well, and some also offer tuition assistance for outside exam courses or even graduate work.
Interviewing in Other Industries
Most of the previous questions are fairly standard, and can be readily found in many interviews for actuarial jobs at any level -- though to be fair, your mathematical skill won't be tested as much if you have a number of exams under your belt. Companies not involved in insurance or pension management will certainly ask about the application of your skills to their particular areas, but you should already be well aware of the answers before you walk in the door for the interview.
Actuarial employers are definitely smart, so your questions likewise need to be smart. Don't ask questions about things that can easily be found on the web site. Do your homework, research the company and ask intelligent questions.