He's obsessed with most of the Wayne heirs.
The most obvious being Damian because he's actually related to Ras, only he's not to thrilled with his grandson and regards him as a failure. I'm not really sure if this is because he chose Bruce or not. I mean Ras did have plans to take over Damians' body so maybe he never cared because of that?
Nyssa briefly took over her fathers' empire only to be killed by a drugged Cassandra Cain. See Cass was trained from birth to be the best assassin. "The one that is all." Ras himself might not have looked into her after she left as a child but he was the one that got David Cain to work on his idea for the perfect killer. She took over the League Of Assassins which splitered since they previously worked for both of Ras' daughters. This leadership didn't last for long and Cassandra was saved from her drugged state.
I think the only time he ever showed interest in Dick was because he was the heir apparent to the Batman legacy. At the end he's pleased with the results and was okay with Dick filling in for the role. Only, I don't think this was ever followed up on. Why? Well Ras became interested in someone else...
After Dick Grayson became Batman and he chose Damian as his Robin effectively kicking Tim out of the role. Tim left to look for evidence that Bruce was still alive. While he was doing this Ras was looking for a proper heir since Damian had disappointed him and Bruce wasn't in the picture anymore. Tim passed all his tests but said no to the offer. Ras thought Tim still made a worthy heir and tried to get his half sister to force herself onto Tim to get a heir. Yes, that was a plan and an attempt was made in the Red Robin title. Thankfully the plot to rape a teen to get a baby heir doesn't seem to be around in DCnU.
After being hunted by the League of Assassins it's been revealed that Jason was chosen to lead them. At this point I can only guess that there are two reasons for this. 1.) Jason is the only one that's able to fight the Untitled because of his training. and 2.) Coming back from the dead is deemed important to a group of killers controlled by Ras Al Ghul.
Basically Ras wanted most of Bruces' kids to run the LOA except for Dick and maybe Damian. The latter because he seemed far more interested in using him than anything else.