Negative questions are more about how a candidate copes. They are about putting the pressure on. Interviewers are certainly looking for honesty in the answers, but if the role involves pressure then they want to know how the candidate copes with pressure.
(Cooper Lomaz Recruitment)

Always answer the 'What are your weaknesses' question with honesty, but be careful in your choice of weaknesses. Don't give a long list. Make sure the weaknesses you talk about are real. Don't just list the classics, like I am a perfectionist. Proving that you have a good knowledge of your weaknesses means you know yourself and are comfortable with yourself. List specific characteristics about yourself, like I have a big group of friends, rather than I am a team player.

It's important to be very open and honest. Don't try to hide things by saying things like 'I encountered this problem, but it wasn't my fault, it happened because I had a bad manager'. Don't be defensive. If you are asked to describe a time you made a mistake, explain exactly what happened and talk about what you learnt and what you would do in the future if faced with the same situation again.
(Office Team)

If you are asked about a time when you have made a mistake or had difficulties, always present your answer in terms of what you learned from the situation. Be careful, not to come across as too practised in the way you answer the question. I have seen people who interview very well, they come across as slick and packaged, but there's a sense they are putting up a front. Interviewers look for honesty, so don't be afraid to inject a bit of yourself into the exchange. Don't be afraid to show that you are human. Don't compromise and don't try to be something you're not.
(Strategic Dimensions)

With any question like 'what would you say your weaknesses are?' employers are testing two issues: first, are you self-aware, ie: are you able to see there are things you are not so good at and secondly, are you the sort of person who does something to correct it? Avoid giving weaknesses critical to the job.

If they ask what salary you require, avoid being too specific. Use a phrase like: 'In the range of...' Try not to discuss salary until you are offered the position because then you are in a better position to negotiate terms and responsibilities. If you are unsure what to answer, bounce the question back if this seems appropriate.

Another difficult question is 'describe a situation where your work or an idea was criticised'. You are being asked to describe how you handle criticism. It is advisable to describe a poor idea rather than poor work. What does matter is how you handled the criticism. So a good answer, for example, would be, 'I asked for further advice, then we worked together to come up with a more viable idea. My manager's input was invaluable.'

If you're asked where you see yourself in five years' time, they're asking what will keep you motivated. To prepare, think about what has motivated you in the past that would be relevant to the job - it could be as simple as knowing that you are doing the job well.
(Working Careers)