Crazyguy: "The greek text at Rev. 5:10 says that that they are to Riegn as priests on the earth, no mention of them being kings and not over the earth but on it."
You may be correct or not to suspect that the WT understanding of this text is faulty. I am not going to debate the interpretation of it.
However, your comments about the NWT being not accurate in translation here is left wanting.
You say, "no mention of them being kings."
It all depends on how the translator wants to go about it. The Greek word in KIT for "they are to rule as kings" is "basileúousin," a present active indicative verb form of "basileu ō," which mean: "I reign over" or "I rule as king." The word for "king" in the Greek text is "basileús." One can see that "basileús" and "basileúousin" are closely related. This means that the NWT did not err by using the word "kings" in the expression. If you were to check other Bible versions, you would find that some others do the same. But you are targeting just the NWT. Why?
Concerning the rendering "over" and not "on" the earth as most other versions do, a fact is that prepositions have a lot more leeway in translation that some believe. True, the preposition "epí" in Rev. 5.10 means generally "on" or "upon" the earth with an enfasis ‘on contact’ as many versions reflect, but it is also true that "epí" can mean "over." If you look at the diagram of prepositions in the KIT, you will notice that "epí" is resting on the oval depiction. You will see that "epí" is not only making contact with the oval, but at the same time the sense of "over" the oval form is clearly visible.
So, it all depends on the angle the translator is seeing in the action. That "epí" can also mean "over" in the genitive (the form found in KIT), I refer you to The Concise Greek-English Lexicon of the New Testament by Frederick Danker which states: "[epí] prep., expressing the idea of ‘hovering’, with gen., dat., or acc. [...] --a. w. gen. on, over... By extension, of authority or control understood as ‘over’ someth.... [...] (In ref. to location fo a biblical passage by story content); before, in the presence of ..."
Conclusion: The alleged inaccuracy of the NWT in Rev. 5.10 on grammar grounds cannot stand under scrutiny. Better stay with the interpretation angle if you want to make sense. It's hard to argue against faulty interpretation.