My brother in-law has been interviewing for a new position within his organization lately and he called me up last week for help with a particular question - "How would you improve the operations in our area?" This is one of those "Danger Will Robinson!" questions, so I thought I would share the wisdom I imparted to him with you.
First and foremost, this question can be asked of you as an outsider (you have no experience with the organization) or as an insider (you are currently working for the organization but in a different area/capacity) or as an insider applying for your bosses vacated job. Each of these situations has a different set of expectations of how and what you will answer and different land mines you must navigate. Let's take the first scenario:
Answering as an outsider - Unless you know the interviewer on a personal basis and have a VERY good relationship with him or her, you cannot answer this question as asked. Even if the organization has some well publicized gaffs, you cannot tell your prospective employer that his or her organization sucks in certain areas, particularly if they are asking about their own unit. Why? Because how would you know what is wrong with this particular unit/department/organization? You just met these people and you are going to tell them how to run their business? Not a good strategy.
The real question being asked is "what is/would be your approach to enacting change in our unit/department/organization?" You should begin your answer with something akin to: "Even with the research that I have done on your organization, it would be presumptuous for me to begin giving advice on a subject I have yet to become familiar with."
From this point you can talk about how you will be a sponge, how you will gather information, and your approach to change. All done in the hypothetical and not using the organization you are interviewing with as an example. In fact, this is where you can throw in your experience in this area. I'll let you take it from here, but remember; telling the Emperor he has no clothes does not normally work in this situation.
Answering as an insider - This scenario is a little trickier because the interviewer expects you to know more than if you were fresh off the street. Unless you have some very specific knowledge that the interviewer knows, or expects you to know, I would still dance delicately around the subject. Even if you do have some specific knowledge, you need to couch it carefully so as to not place blame or cast aspersions on anyone. I still like the idea of saying that you do not have enough information to specifically answer the question however if approached with certain problems, this is how you might go about handling them. Keep in mind you should always start your answer with the need to gather information first.
Answering as an individual applying for a vacated position that is higher than yours - This is an ultra dangerous position to be in and you have to size things up pretty quickly. Even if the interviewer states to you that the previous holder of the position performed poorly, you need to make sure you do not come across as a vulture. You are not there to heap criticism on anyone. That is why it is important for you to know or ask as soon as possible in the interview if the person that held the position left on their on volition or not.
In the perfect scenario, you would have gathered your intelligence up front and not have a need to ask, but if for some reason you do not, you can safely gather this information by asking the interview a question like "what kind of shoes are you filling by taking this position?" This gives them an opportunity to give you the necessary information without being blunt about it.
Once this is determined, you can take your answer in a couple of directions. No matter which direction you take though, you cannot feign too much ignorance or you will come across as someone who doesn't pay attention to his/her environment. The first direction you can take is one in which your boss performed well and was either promoted or moved on to greener pastures. In this case you can talk about building on their successes while at the same time throwing out some positive ideas on change. Whatever you do, do not bring names or personalities into it (try to keep the conversation at a level above that) and by no means talk about letting people go etc.
The second direction is one in which the person that came before you performed poorly and you and the interviewer know it. You still cannot sit there and criticize your predecessor. Again, you need to be positive while at the same time using the opportunity to talk about how you could potentially change things to set things right. Again, approach the situation on how you institute and manage change.
Whatever you do, do not lecture the interviewer! Give enough information to get your point across without getting too wordy. In all cases, watch the eyes and the body language of the interviewer and be prepared to adjust your answers accordingly.
From the leadership perspective of sitting on the other side of the table, a question like the one I have been discussing is intended to show how you think on your feet, if you have any tact or diplomacy, and how you handle new situations. A deft answer lets me know that the interviewee knows how to handle difficult questions. A poor answer, or worse an answer that is tasteless and untactful can blow the interview - because this will make me wonder if the person can be trusted to answer similarly touchy questions independently. After all, my employees are a reflection on me - particularly my hires.
My brother in-law was in fact asked a similar question and he feels he did ok. Only time will tell as the interview process is still on going. I hope the discussion above is helpful to you no matter which side of the interview table you sit on.