Interview questions are tough to answer when they ask you to go negative on your current job, isn't it? Going negative on interview questions, after all, makes you look negative. On top of that, any negativity towards your old supervisor is immediately viewed as you not willing to work towards the department goals.
Answering interview questions like "What did you like least about your last supervisor?" the wrong way can help you lose the job.
What these types of interview questions really ask
Part of what happens in a face-to-face interview is determining what style of management you prefer so as to produce your best work. If you work best with a detail-oriented person, working with someone who lets you do your thing your way without a lot of guidance will be frustrating for you.
Consequently, a great manager will bend their way of working to the way you work best -- or they won't hire you. Just as important, you need to know this so you won't go crazy working for someone who doesn't match your best way of working. It is a subject that can't be ignored.
To answer, describe the management styles
No one will ever match up to your "best way" to work with you. For these types of interview questions describe how your supervisor practiced management of his or her employees. Factual; not loaded with emotion.
Then, contrast this with how you like to be managed to produce your best work. Note the differences between how you were managed versus how you would like to be managed. The best way to do this is in some element of the format of "more of this" or "less of this."
"My supervisor wanted to work through issues until all points were researched and heard. The way I work best for a manager is to get to some point of consensus and then try some testing to determine what approach would work. For me, it would be better if we did more testing of concepts to prove their workability."
Then, describe how you made adjustments to work well together
Since no person will match perfectly with your best way of working, you also must answer these types of interview questions with how you adjusted to your supervisor's style so you could work well together. Unfortunately, in many cases, you'll be the one doing the adjusting rather than a manager adjusting to you. Thus, you need to describe what you did to adapt and how you worked well together based on this change.
Showing how you adapt is a key way to show that you can work with the new manager and your new coworkers. It shows you being a flexible person and one that is willing to change to match up in a different environment.
How much are you willing to adjust?
To be clear here: you have to decide how much adjustment is worth it to accept a job offer. Compromise away your principles and putting up with styles you dislike is a recipe for disaster. You need to determine the manager's style. You have to get your needs out there as well. Then the hiring manager and you have to figure out if you can each adapt enough to each other to work well together.
What kind of management style produces your best work?