how will you deal with a situation where you disagree with someone you manage who has more expertise on a particular area than you do?
I'd listen to their pov and that of others in the team and once I'd taken all points of view into consideration I'd make my decision. As the manager I should be able to make decisions that not everyone agrees with because ultimately I will be responsible for the outcomes. I would explain my reasons and would expect my team to appreciate that sometimes we will disagree but we will do so calmly and with professionalism.
- how will you deal with a situation where the experts you manage (and maybe you) think x and y should be priorities but senior management (and maybe you) think a and b are?
An important part of a manager's job is to make sure the team understand the priorities of senior management and ensure that team priorities are the same. If as a team we thought a and b should be priorities then it would be reasonable to bring this up for discussion with senior management but ultimately, senior management may have access to other information which has helped them decide their priorities and so their priorities must take precedence.
- how will you deal with poor quality work?
It depends on the reason for the poor quality. I'd want to look at that first.
i.e.
was the task/objective specified inaccurately?
Was the person empowered to perform the work and given the tools they needed? Did they have access to everything they needed to do it?
Was the timing right - i.e. did they have enough time to do it and were the deadlines reasonable?
Are they skilled enough to do it?
Was there another reason for poor quality/underperformance?
Does the person need training? Redirecting? Are they the right person for the job? Sometimes people just are in the wrong jobs and so you need to manage underperformance
And once I'd established that then I could pinpoint what had gone wrong and how it might need to be addressed differently next time.