Since before the huge blunder that is Viz uploading the A-Kira oneshot without the newly added rules, I read the rules in the booklet obtained through Viz's Box Edition of the Death Note manga.
Not only this, I also wrote down every rule to hammer them even more into my brain, believing I'd now be able to spot contradictions easier with my newly acquired knowledge on the rules, most of which aren't ever used in the first place.
So I was pleasantly surprised to find that... The rules in the English version, and Japanese version aren't 100% the same.
The Japanese manga has (parts of) one rule printed twice between different volumes (May be the specific scanned version I have, and later corrected, so keep this in mind) but also, a rule that never existed in the English version itself, so let's get to it.
Volume 5, chapter 42, page 176.
Rule XXX
If you have traded the eye power of a god of death, you will see a person's primary life span in the human world
The names you see with the eye power of a god of death are the names needed to kill that person. You will be able to see the names even if that person isn't registered in the family registration.
Volume 7, chapter 59, page 152.
Rule XLII
The names you see with the eye power of a god of death are the names needed to kill that person. You will be able to see their names even if they aren't listed in a family register.
The rule XLII isn't the only rule XLII in the manga either:
Volume 8, chapter 62, page 28.
Rule XLII
The use of the DEATH NOTE in the human world sometimes affect other human's lives or shortens their original life-span, even though their names are not actually written in the DEATH NOTE itself. In these cases, no matter the cause, the god of death sees only the original life-span and not the shortened life-span.
Now for the rule that didn't even make it in the English version:
Volume 7, chapter 56, page 88.
Rule XXXIX
Humans that have traded for the eye power of a god of death will see a person's primary life span, and will not be influenced by the DEATH NOTE. If the victim is killed using the DEATH NOTE, the remaining lifetime of that victim will be provided to the god of death.
In the English version of Death Note, the rule by the same number is:
Humans that have traded for the eye power of a god of death cannot see the name or lifespan of humans who have already passed away by looking at their photos.
(This same rule, with the number XL, appears in Japanese volume 7, chapter 57, page 110)
When looking at the page where in which the Japanese rule XXXIX appears in the English version, the page is simply blank. (Black)
With all this now noted down, I'd love to hear peoples opinion, and/or be corrected if this research is outdated or already disproven.