RYbs noted that the ikkur problem with hashgachos (among the good ones) is not their standards (you may discover that many of the hechsherim on the list have stellar standards), but rather, the enforcement of those standards. This is in direct contrast to the US where, among the good hechsherim, the enforcement is often excellent but they may choose to apply some wild kulos.
He allows Eida (Badatz), Rubin, She'eris and Landau to be served in the shul.
My personal collection of psakim from him are as follows.
Re: Cholov Yisrael - there is a preference to buy only Tenuva-brand Badatz for milk products. However, where product, price or convenience are not equal, he said I can use any Eida (aka Tara brand), Tnuva Mehadrin (the double hechsher), Rubin (Strauss brand and that random blue-labeled company that makes goat milk products). Other people have received stricter instructions than me; but I repeatedly ask him about this and get the same answer.
Re: Rav Efrati: there is a preference to buy otherwise but we use him on Shemitta when he has Chul products. (We don't use ANY greenhouse products on Shemitta when they treat it as non-Shemitta - RYBs is concerned their system has holes (pun intended).)
Re: ZNT - not currently recommended.
Re: Iggud Harabonim, Manchester (Rav Westheim Z"L) - RYBs said we can use him on products from outside EY but not on products from inside EY.
Re: Kehillos - "Ask Rabbi Kuber." Rabbi Kuber is currently not enthusiastic about Kehillos.
Re: Bet Yosef - Their chicken is shechted in the same facility as Eida chicken and by the same shochtim. Nevertheless, unless we are stuck, preferred not. (This is said to be because of the shidduch prospects of our kids, or something.)
This should not be said to be a rejection of other hechsherim on the list (though none make it into the top category), but this is what I was mekabel from him in conversation.