Moveaway laws that prevent the mother from moving for any reason yet do not affect the father even if his move completely disrupts visitation. They don't get much, they don't get what they are awarded, and it isn't enforced. Also, an abuser can use mediation to control his partner, intimidating her to do things his way. Mediators focus on getting an end result, regardless of whether or not that result is in everyone's best interests. It's also possible a woman may not learn of her legal rights with a mediator.
Training is a problem as well.
Anyone can throw out a shingle and work as a mediator. There needs to be some quality control. Friendly Parenting Provisions, which relate to custody. The parent who is deemed more likely to encourage the relationship between parent and child is the one who should get custody. This one came about primarily due to mothers who either experienced domestic violence or strongly suspected child abuse and were either very reluctant or outright refused the father access to the children.