This is a relatively common situation:
SITUATION: During a non-refereed doubles tournament match, Team A accused a player on Team B of using an illegal serve and, separately, a double bounce. Team B denied it.
QUESTION: In a game with no referee, can the receiving team call illegal serves or double bounces on their opponents?
ANSWER: They can attempt to call them on it but both teams need to agree - one team cannot unilaterally make such calls on their opponents. Rule 13.D.1.b says: “Players may call the Non-Volley Zone faults and service foot faults on the opponent’s side of the court.” (Notice that illegal serves and double bounces are not included.) If available, a team may request a referee to call the match. However, most people are honest and common sense usually prevails. Click here for an interesting video on this topic entitled "How to Deal with an Illegal Server" by Mark Renneson.
In this particular situation, Team A requested a referee observe the server on Team B. A referee observed their next game but saw no illegal serves by any player. Team A later informed the referee that, once he showed up, the Team B player cleaned up her serve for the remainder of the match.