The weaknesses you should tell an interviewer include those that don't relate to the essential skills of the job you're seeking and those that you have improved on during your previous job, according to About.com. You should aim to turn any weaknesses into strengths.
As an interviewee, you should examine the essential skills for the job in question and create a honest weakness, which does not essentially affect the job. For instance, if the job involves dealing with clients one-on-one, you can say that you are weak in dealing with groups.
When mentioning the weaknesses that you have improved on, you should include the weaknesses that you experienced while you were under your previous employer and discuss how you dealt with them to improve the situation. This proves to your potential employer that you have the ability to change and improve yourself as needed. To prove this, you can tell the interviewer your previous level of a skill you were weak in as well as your current level of the same skill after the improvement. However, you should take care to avoid mentioning skills that you improved on and are essential to the job you are applying for, as this may make the interviewer doubt your qualification for the job.