Harry makes surprisingly few great decisions in Harry Potter and the Half-Blood Prince. From choosing to follow mysterious instructions in an old potion book (including random, handwritten spells), to failing to collect a memory from Slughorn time and time again, to obsessing over Draco's status as Death Eater (to no purpose), Harry's Sixth Year may be one of his least productive!
Despite this, though, he is the Chosen One - and that means he has to make some good decisions along the way, too. Fitting, for a book (and movie) that introduces Felix Felicis, many of his best moves come down to sheer luck - but some are a sign of an intelligent mind, too.
Following The Instructions In The Old Potion Book
While this may seem like a truly terrible idea, especially given the way that things turned out the last time Harry got involved with a mysterious handwritten book (Tom Riddle's Diary), it actually turned out to be a great move. His choice to actually follow the handwritten notes, instead of the main instructions, led to him winning the Felix Felicis potion (which would come in very handy), but it taught him a great deal. It even clued him in to the use of a bezoar when an antidote to poison isn't readily available, which would save Ron's life. And on top of all that, "his" impressive skills as a potion-maker were a key part of his ability to forge a bond with Slughorn, that would later lead to him getting the vital memory. Had Harry chosen to follow the original instructions, as Hermione pushed him to, things would have gone terribly wrong this year.
Tricking Ron With Felix Felicis
While this plays out slightly differently in the book and the film, in both, Harry tricks Ron into thinking that he's been dosed with Felix Felicis - to give him confidence on the Quidditch Pitch. He hasn't, of course, and it may seem like a bad choice to deceive a friend, but this is actually one of Harry's better moves this year.
On the surface of things, this allows Ron to regain his confidence as a Quidditch Keeper, helps Gryffindor win their match (and go on to perform well in future matches), and keeps the odious Cormac McLaggen off the team, but it does more than that. Ron increasingly struggles with jealousy, and his role as a star Quidditch player this year gives him some space to shine on his own, not just as the sidekick to the chosen one.
Turning Down The Ministry
One of Harry's biggest decisions this year is to (repeatedly) turn down the Ministry when they ask him to make a show of solidarity with them. While this decision may be something of a knee-jerk reaction to the way that the Ministry treated Harry in the past (both with sending Umbridge to the school and with trying to discredit Harry in the papers - it was a wise decision on many levels.
Not only is Harry choosing to strike out on his own, rather than looking for Ministry support, but the Ministry is riddled with Voldemort's people. Almost as soon as Dumbledore dies, the Ministry falls - and had Harry put any stock in them, this would have been a disaster for him in the long run. Of course, it's also deeply satisfying to watch, too!
Taking Ron To Slughorn When He Is Lovesick
In some ways this may seem like another bad decision - after all, Harry takes Ron to Slughorn to cure him of a love potion, and he ends up near death thanks to poisoned mead! However, this was still the right thing to do! Harry had no ability to fix an antidote for Ron himself, especially given the fact that the love potion was incredibly strong, and the longer he left Ron in that state, the worse things could have become. Slughorn, as Potions Master, was a great choice of teacher to go to for help (although Snape would have been equally good, if not as kind about it).
However, it's also this moment that leads Slughorn to open the mead, and discover that it is poisoned - instead of passing it on to Dumbledore as planned. While it's not guaranteed that Dumbledore would have actually consumed it (and of course, he was dying anyway, at this point), Harry may well have prolonged Dumbledore's own life for long enough to learn how to defeat Voldemort himself.
Using Felix Felicis On Himself
Clearly, his most intelligent move in the entire year is when Harry takes the Felix Felicis in order to try and get the vital memory from Slughorn - and then follows the push that the potion gives him! Presumably, given the magic of Liquid Luck, Harry would have been able to get the memory he needed no matter what... but only if he had found Slughorn in time. And had Harry not taken the potion at all, based on his previous clumsy failures, he would have found no other way to get the memory.
Instead, the decision to take the potion, and then to ignore Hermione's urging of what to do immediately after, was what led to his interesting evening with Slughorn and Hagrid... and finally learning how many Horcruxes Voldemort had made. Without this vital piece of knowledge, of course, the entire remaining battle against the Dark Lord may have failed.