Simple questions :
- Where are you based, and are you legally able to work where you're applying without too much overhead? Sometimes a company may like you but not be willing to jump through hoops after they realize how hard it will be to hire you, in which case they still interview to check if your talent justifies the hassle.
- Are you always on time, and always replying fast to emails? Lack of punctuality hurts bad, especially in a management role.
- Do you have a tendency to blame your current environment or your co-workers in interviews? No one wants to work with someone who's going to blame them or their company.
- What do you answer to the classic "where do you see yourself in 10 years?" Interview questions? This has a very strong impact on any large company.
- How long did you stay in your previous and current gigs? Job hopping can be a red flag.
- Did you ever get to the salary negotiation phase? If so, were you the one asking first? A candidate asking for too much might not look attractive.
- What is the size of the organizations you apply to? Your experience might not match what they're looking for.
- How do you define product management? Product Management is such a wide net (Design / Management / understanding of tech/...) that what you're currently doing and what the companies are looking for might not match. This happens more often than we could expect.
To anyone else reading this, but looking for a programming job (and not product management like OP), add those questions to your list:
- Do you contribute to open source? A lack of contributions will prevent your interviewer from selling you properly to a team.
- How good are you with algorithms and data structures on a whiteboard? This is like a sport, and as backwards as it is, it is different from actual programming, so you should actually train interviewing as a separate skill if you're not proficient.
Finally, 15 interviews for 50 application is not terrible, answer those questions honestly and you're probably going to do better!