I once questioned the same things, as far as the possibility that Jehovah is ok with the org making mistakes, as he seemed to be ok with it in the past. That was until I decided to read the bible. Is so plain and simply put that it is impossible to ignore. You can only not see it if, commanded by the org, you refuse to "engage in independent study of the scriptures". Reading the bible on our own can lead to apostasy, says the WT. That alone should wake most people up but when you realize it doesn't, then you must questions what we are really following.
As far as the comments other have posted. Well they are totally right. I myself still believe in God. I am not a dogmatic person anymore, but I do believe. I respect those who don't and I am convinced that God does too. You see, we were once JWs, but we did not really understand the concept of "bearing witness". As JWs we are thought time and time again to put faith on someone's apparent appointment as the FDS but such individual can not "bear witness" of their appointment. In other words, they can not perform any kinds of supernatural act that will convince us that they indeed have God's approval. As JWs we fail to study, and therefore fail to understand, that such concept is plastered all over the bible. Yet, we will probably gravitate towards the "blessed are those who believe without seeing" very easily. Everything in context, you will realize that there is no faith without manifestation. In other words, there is no faith without the witness of works by the holy spirit. Yes, faith is an expectation for the future, but is based on the experiences of the past. Its sort of like your credit score.
So to sort of explain how I answered the same question to myself. I would be willing to accept the mistakes and imperfections of the org so long that they can proof that God has really appointed them. If God has forgiven them and continued to cast his blessings over the org, then it should be fairly evident. If such happened, then I would understand that whatever mistake was made, it was an honest one and they should be forgiven for it just like we are forgiven every day. As many pointed out here, there is overwhelming evidence to the contrary. Simply compare the story of David. Just because David did a handful of sins, they do not overshadow the other good things he did. I am not justifying his actions, I am just comparing it to the modern idea of the "kingdom". If his were honest mistakes, then God will decide what to do with it. I am no judge on that and if David was alive today, I would not disagree with him paying for what he did under secular law. In the same context, Jesus spoke very clearly on how hypocrisy was more important to him than sins themselves. And this should be very easy to see, as the golden rule would apply to this. As JWs we tend to interpret the golden rule as something that only applies to good deeds. While it is true, it is also true that is a good ruler to measure wrong doing as well. Jesus never dismissed some of the things the Jews commanded as being wrong but he rather showed how they should not impose if they were not willing to do that themselves. Sure some of the rules were unjustifiable, like not healing on the Sabbath but in other cases he showed that the rule itself wasn't unreasonable, so long it was applied in the right context and so long the ruler was willing to apply the rule to himself.
If the prophet Nathan came today to speak to the GB and pointed out their flaws as he did to David, he will be Dfed on the spot.
Hope I make sense. If not, I can explain myself further