If you hear this question, it’s a sign that you are being considered seriously, because asking you to evaluate your past supervisor is a way of checking on several important character traits at once. It simultaneously tests your loyalty and your honesty by checking to see how you will approach the issue, and it also allows the interviewer to determine how objective and evidence-based your judgment is, which is a way of checking your temperament as a decision-maker.
When you answer, think carefully and take your time. Also, consider the following ideas.
Try to show how your suggested improvements show how things could be done better without emphasizing negative aspects of the current process.
Keep things positive by highlighting the weaknesses in neutral language, with suggested alternatives that would enhance their leadership.
Focus on the professional, and make sure that each critique has to do with their performance within the job.
Approach this as a way of showing what you think your boss modeled well and where your personal philosophy differs, so that the interviewer sees that you are aware of the options in other leadership styles.
As with any question that asks you to provide criticism, it is easy to go too far with this one. It’s also easy to avoid going far enough.
Never launch an attack on your previous boss. Make sure you answer the strengths part of the question, no matter how you might feel personally.
Similarly, you want to avoid making any evaluations based on personal habits or quirks that don’t affect the job.
Overly positive answers are also trouble, because they neglect to show what you learned in a way that highlights your readiness to move up.
Don’t let yourself slip into informality. Informal language can sound disrespectful even when it isn’t meant that way.
Here is one way to approach the question without being caught in any of the mistakes listed above.
At my last job, the supervisor was great at communicating about the work process and timing, but conflict resolution was a bit of a problem. If two departments went head-to-head over the same resources, he rarely intervened to settle the issue, so the process could be a bit drawn out. It gave individual workers a bit more chance to be heard, but I’m not sure I’d let things go that long if it was me, but I would certainly make sure I heard everyone before speaking up.
That answer makes sure to point out the interviewee’s knowledge that the difference is partly stylistic, and not all a matter of black-and-white.