Is a "polite compliment" necessarily a redundant statement when used in a group of people as opposed to a one-to-one situation?
I disagree with the other answers. A polite compliment is one that is both flattering and delicately phrased. For example, the following is in essence a compliment, but is not in any way polite:
The fictitious speaker is trying to express an aesthetic admiration for the particularly beautiful breasts sported by a woman he is looking at. It is an expression of a positive judgement of her physical appearance and is, therefore, a compliment.
However, in our society it is not considered very polite to compliment the appearance of the sexual parts of the human body. Even if it were, using as vulgar a term as rack (which is the least vulgar I could come up with in this context) is definitely not polite. Such a "compliment" will not be well received unless the speaker enjoys a very intimate relationship with the woman in question. I would not recommend it even if that is the case though.
Alternatively, what if someone were to compliment Hitler while talking to a survivor of the Holocaust? While he may well be paying Hitler a perfectly decent compliment, his interlocutor will, at the very least, not find it very polite.
Merriam-Webster's relevant definition of compliment is
That does not mean that a compliment need be polite, only flattering to at least one person. I would understand a polite compliment to be one that is both flattering and phrased in a polite and delicate way.
All compliments are ment to be nice and polite...but one could say "polite compliment", that would just mean that compliment was extremely polite.