I'm a fan, a coach, a parent, and a referee, so have seen a lot of soccer at various levels, from recreational U6 to pros. I've only refereed club soccer as high as U16 SDDA games. I hold the U13 referees to the standard for that level, meaning they should be able to recognize all fouls, and know the laws. Their mechanics should be sound, and they should be communicating with the players and coaches more than you may see in U10, but not as much as a seasoned referee much higher (see the Australian dude's communication in that 4 minute video recently posted).
I saw one referee do a dropped ball twice in two minutes, dropping the ball from his chest height. I saw many referees not trying to stay near play during hotly contested games. I saw zero mirroring by the ARs in one game with the referee not being in the correct position to see the AR1, leading to missed offside calls and missed calls for subs. I saw one goal disallowed for offside, even though the ball was obviously played by a defender.
Look, I work with AYSO referees (am an instructor), and realize that because they are volunteers, I cannot ask for too much from them, just hope that they are there. Then hope that they help keep the game from getting out of control, and help ensure that the kids have fun. That's about it.
For paid referees, I hold a much higher standard. They should know the laws inside and out, and should have the mechanics down. Run a diagonal, stay close to play, and keep an eye on the ARs. The rest will come with experience (better foul recognition, and the ability to communicate more).