There is a difference between highlighting your positive points to make yourself different from others and lying to the interviewer. These days the organizations are very particular to check the authenticity of the candidate, by doing reference check or background check, so you should not land yourself into trouble by saying something which would not be verified by your boss or the references that you offer.
The most severe way to induce you into trouble during an interview is telling a lie. There can be many other ways to land you into trouble. The most common mistake is lying about the educational degrees that you don’t have and taking credit of the work that was not actually done by you, for example saying that you are a manager when really you are a team lead. All of those things may sound sensible at the time of an interview, but what if the interviewers cross check your work with your boss for which you took all the credit in the interview. Your boss isn’t aiming to lie for you and if you were still with the company, you won’t be there any longer.
The best way to handle these situations is to inform the reality, and place you in a safe zone. Share the success of the project in which you were involved. The employees who acknowledge and share the success of others are more desirable candidates for the position than those who want all the praise for themselves. This doesn’t mean that you have to be compelled to give the share for every work you did in the organization and doesn’t place you in an exceedingly positive position. The only thing to remember is to be honest and solely point out examples that are aiming to highlight your skills and work history in the best manner. Don’t claim or state anything that can’t be saved by your references during background check.