Yes, there are a few things that immediately come to mind as red flags for interviewers. I have observed all of the following at interviews and these points have come up in discussions with my fellow interviewers after interview:
Speaking negatively or in a disparaging way about a previous manager or employer
Breaching the confidentiality of a previous employer
Being disrespectful of other nationalities in your answers.
Some other common "red flags" are:
Rambling in all your answers
Not answering the question asked (repeatedly)
Taking an excessive amount of time to give the context to all the examples
Contradicting yourself or what you wrote on your application
Not seeming to know anything about the role and/or organisation
Exaggerating your answers (and that being shown up through your answers to follow-on questions).
Tina's Blog - Interviewer Insights
My interview tips are based on my years of interviewing experience and my years of interview coaching.