Should I keep an eye on my bf as he stares at other women sometimes?

While on vacation I noticed my bf eyeing up other women and at times chatting them up whenever I wasn't around. This annoys me because I paid for his trip since he's not in a good spot financially (he has a good job but is paying a lot in child support and his ex wife left him with a big house, new car and high mortgage). He isn't outright flirty with or hitting on other women or anything like that but he will make eye contact with them until they chat him up and then he will be friendly back. Should I keep an eye on him?

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