Several things here:
- If you don't have enough time, it is always fine to ask the interviewer in a polite manner to repeat what he just said. Basically, you have no choice.
- Another way is to increase the speed of taking the notes. Use acronyms, and practice to write short descriptions.
- Make a recap - usually, I recommend making a recap after asking clarifying questions, but in your case, it may be beneficial to make a recap right in the beginning. "Do I Understand correctly that..."
There are some questions that you should always try to ask in addition to what he told you:
1) You can also ask the interviewer to tell you more about the business model and how the company generates money. Even if you think you understand it, try to repeat it to make sure that you understand it correctly. e.g. if the case is about oil&gas company which revenues are declining, ask if it is Up / mid / down-stream problem. In this case, defining a revenue stream is critical to setting up the right structure.
2) Clarify the objective. Here make sure that your goal is:
- Has a time-framed
- Has / has no limitations
e.g. Should I invest 100k in this business for 1 year if I want to get 15% return?