Hopefully someone will come along with more knowledge than I have, but I recently finished up the recruiting process for a full-time Finance/Accounting position, so I assume the questions might somehow be similar to those for the Professional Internship. In addition to the standard behavioral questions, we had a case study. I think the exact contents of the case are confidential, but basically they had us walk through a real-world business scenario and asked us to consider all possible factors that would influence our decision making. There were a few equations to work with, but nothing more challenging than what you'd see in Principles of Microeconomics/Principles of Finance/Managerial Accounting I.
Of course, there's a chance that the Professional Internship doesn't have a case interview, but I'm not sure if any of the Interns on the boards are in the Finance/Accounting roles, so I figured I'd offer my personal experience. In other non-case Finance/Accounting interviews I've had, I've found the following pretty useful:
1) Knowledge of the company's diverse sources of revenue (for Parks and Resorts: gate admission, food and beverage, hotels, merchandise, tours)
2) Knowledge of the company's diverse expenses (for Parks and Resorts: labor, food costs, resources and utilities, cost of goods sold)
3) Ask questions and think out loud
4) Basic business mathematical concepts including break-even analysis, sensitivity analysis, etc.
5) Strong handling of all of the concepts covered in your 'Principles' courses. They're not going to ask you about material from Advanced Measurement and Disclosure, but they might ask you about simple GAAP concepts (capitalization vs. expense, for example), or certain Excel skills
6) Expect to hear a question like the following: Project X will cost $Y to build and $Z to operate. How would you go about determining if such a project should proceed? They're looking for you to consider all aspects, including initial investment, operating costs vs. revenues, and (perhaps most importantly) hidden costs and revenues, such as increased merchandise sales from a new attraction
I hope all goes well and we'd all love to hear back from you as you go through the process.
Good luck!