[Numenorean]

Formy -

The interesting thing to note then, is that of the Rings, the ones given to the Dwarves were ultimately least effective. Is this because, as an almost-kinsman, Sauron was blind to the faults that would turn a Dwarf to evil? Or is the simple fact that Sauron's rings were effective at all proof of his insight?

Hmm, I reckon that either through his Aulëan heritage or via his own dark observations, Sauron had a fairly firm understanding of what could lead or turn a dwarf onto an evil path, it was the complete domination of their wills that he could not fathom. However, just accepting one of the Seven was enough to assure a dwarfs doom, in this respect Sauron was akin to his old lord Melkor in that whatever they could not utterly dominate, they ruined.

Thinlómien -

I'd say that greed is their worst sin/trait/fault. That can be read numerous times from TH and LotR

Good point, avarice is indeed a potent and negative force in the Dwarven psyche, linked to but not entirely dependant on their pride, and when we read (in LoTR Appendix A III) that:

"The only power over them that the Rings wielded was to inflame their hearts with a greed of gold and precious things, so that if they lacked them all other good things seemed profitless, and they were filled with wrath and desire for vengeance on all who deprived them."

It could even be argued that Sauron was at least semi-successful in his Dwarven Ring lore, as some power and influence over the bearers of the Seven is surely better than none at all. The last two bearers of the last of the Seven to be retaken by Sauron, Thrór and Thráin, did not, it would seem, remain entirely uninfluenced by the Ring. Intriguingly it is said in the LoTR Appendix A III regarding Thrórs motivation to single handedly attempt to regain Moria that:

“He was a little crazed perhaps with age and misfortune and long brooding on the splendour of Moria in his forefathers’ days; or the Ring, it may be, was turning to evil now that its master was awake, driving him to folly and destruction.”

And of the last bearer, Thráin, shortly before he went forth into the Wild and met his doom in Saurons dungeons at Dol Guldur, the following is said:

“It was therefore perhaps partly by the malice of the Ring that Thráin after some years became restless and discontented. The lust for gold was ever in his mind.”

Kuru -

One other thing about the Rings…it seems likely that the Eastern Dwarves would have received their Rings from Sauron himself as the Eastern Houses probably had little contact with Elves (particularly not the Elves of Eregion).

Interestingly enough, (and only on a slight tangent) the Dwarves of Durin’s Folk believed this Ring of Thráins was the first of the Seven to be made, and that it was handed over personally by the Elven-smiths, specifically Celebrimbor, to King Durin III of Khazad-dûm himself.

Kuru -

In the case of Men, the Rings performed admirably and as Sauron intended. In the case of the Dwarves, they did not work as Sauron intended. In the case of the Elves they didn’t really work at all. I think from this evidence, one might conclude that Sauron had more of an insight into Men than anybody else.

Don't forget that there are strong examples of Men who resisted Saurons influence (Amandil, Elendil etc) so his insight into the hearts of the Atani was by no means complete. I would agree though that the race of Men – generally - are more corruptible and susceptible to Saurons evil guiles, though maybe thats more to do with Mans inherent weaknesses rather than Saurons strength of insight. He may have known decidedly more about Dwarven lust and motivations, but their inherent secrecy, stubbornness and indomitable will neutralised the potency of his attempts at manipulation thus, as you say, his Dwarven Ring lore did not work as Sauron intended.