By 'others' I assume you mean the other Friends aka Monica, Chandler, Phoebe and Joey. None of them were aware that they were going to get married since they spent most of the evening alone in their hotel room getting drunk. The first time they were aware they were getting married is when they received a phone call from them and by the time Phoebe and Joey arrived at the Chapel, they had already got married. Monica and Chandler didn't know anything about the marriage until the second Rachel and Ross came out of the Chapel.
If by 'others' you mean the people that officiated the wedding, there's no law against drunk people getting married. In fact, as far fetched as Rachel and Ross' marriage seems, it DOES happen. Vegas is a place where getting married is readily available, throw in some alcohol and the general "throw caution to the wind" and "YOLO" attitude that most people adopt when in Vegas, and drunken people getting married on a whim is more common than you'd think.