Sort of a two part essay on Harry's probable ligilimense ability and how Riddle exploited it thru Nagini...
I get the feeling that Harry truly is a ligilimens (but not an occlumens), but just doesn't realize it yet and why there's still plenty of evidence that Riddle had some outside help in attempting to possess Harry in OotP...
Harry often has deep insights into others, not just Riddle. When he started to have "visions" of Riddle's actions, it's a clear sign that he knew what was going on with Riddle, but that there is weak evidence, if any, that Riddle could ever truly see inside Harry's mind. Riddle only sensed Harry's presence inside of his and I suspect that prompted him to try to possess poor Harry and use Harry's insights as a weapon against him.
Enter Nagini...if Nagini is one of Riddle's horcruxes, it is very possible that Riddle used Nagini as an aid in his attempt to possess Harry as early as GoF, which explains Harry's horrible nightmare at the beginning of GoF and subsequent startling knowledge of Riddle's movements. Possibly Riddle planted Nagini somewhere at Hogwarts or near Hogwarts grounds to track Harry and if Nagini is a horcrux, maybe that was the part Harry was picking up and was leading to Riddle's thoughts and feelings. Perhaps Nagini, in her being part of Riddle, then had the thoughts communicated to Riddle on what Harry picked up. Nagini could have also been on Hogwarts grounds, maybe even sneaked into the dorms without anyone's knowing it and that's maybe what made Harry's scar hurt so much in OotP.
That also gave Riddle to idea to try to possess Harry thru Nagini. Naturally, we saw how that attempt failed in the showdown in the Ministry, so Riddle gave that up and knowing that Harry is a ligilimens and a very smart one at that, Riddle decided to use occlumens in HbP. Riddle probably is really not a ligilimens. A good occlumense, yes, but not a ligilimense.
Now Harry, on the other hand, is not an occlumens, but I suspect he's a ligilimens and that may be a key to his defeating Riddle in the end, being that he will probably need to enter Riddle's mind once again and destroy Riddle's power and get out quickly again (there is the danger that Harry could wind up like Neville's parents).
I get the feeling the alleged "link" Riddle claims to have with Harry is not really out of ordinary or unprecedented as many ppl. thought. I think Harry's parseltongue and all is not really anything more that any "connection" Remus Lupin has with the werewolf who attacked him as a child.
And add in their wands...Harry and Riddle's wands could be significant since they both share have the feathers from the same phoenix...if Harry doesn't use ligilimense, Harry's wand could be actually the "key" to enter Riddle's mind and carry out the final mission.
Going on the rich psychology of the books, the wands "choosing" the person is indicative of the wand sensing the personality and memories, however subconscious, of the wizard or witch. I think Harry's wand feathers were smart; they sensed Harry's subconscious memory and trauma of losing his parents thru Riddle's attack and that Harry would be wanting to destroy Riddle's power; the wand maybe saw what was in Harry's mind, even the subconscious memories. Ditto the wand for Riddle and many others. I suspect that's what Ollivander meant by the wands "choosing" the buyer.
Comments? Questions? Agree...disagree and why if disagree? Did I leave anything out?