have your/its moments
have its/(one's) moments
To have particular instances in which one is better or can be seen to have more value, especially when that is not always the case. The movie has its moments, but overall it was pretty boring. You and I had our moments when we were together, but we always ended up fighting. We just weren't meant to be. A: "I really can't stand John." B: "Oh, come on, he has his moments."
have your moments
1. If you say that someone or something has their moments, you mean that there are times when they are successful or interesting, but that this does not happen very often. The film has its moments. Jose probably isn't as talented as Mitch, but he has his moments.
2. If you say that someone or something has their moments, you mean that they sometimes do bad things or cause problems. Dick has his moments and he can flare up, but it's usually when he feels his authority is being challenged.