Zd,
They also give hashgoha to restaurants with mixed dancing
No they dont, they are actually quite strict on many things, ie they will not give Haschgacha to places open on Shabbos owned by a Goy (Even Ice Cream Stores)
In fact when a potential convert goes to Rav Belsky, He tells them to go to the Vaad of Queens (They are the ONLY place in the US that has a real convert program)