It seems like every topic that is read has a least one person referring to Naruto as an idiot. Though he may be lacking in common knowledge of the Ninja world (due in part to allowing the reader to learn along with him), he has shown a mind for combat. This type of intellect would be of the demand type, rather than academic, meaning that Naruto's smarts are triggered by need, rather than by want. Below are some of his moments of brightness:
Zabuza - Using a mass amount of Shadow Clones to hide his true objective, which was to disguise himself as a Fuuma Shuriken and get it to Sasuke, in a way that allowed Sasuke to understand the plan, without letting Zabuza in on it. This demonstrated both an understanding of Sasuke's psyche, to know how he would react, and the ability to think ahead multiple moves, forseeing even as far as Zabuza dodging the shuriken, allowing Naruto's surprise attack to free Kakashi from the water prison.
Neji Hyuga - Planned out moves and psychology were also seen in this fight as well, using shadow clones for misdirection once again. By intentionally keeping one clone back, Neji was drawn to attack it, believing that it was the true Naruto, keeping his distance from danger. In doing so, Neji left himself open to the real Naruto, by giving up sure footing for what he believed was the final blow. Naruto also used the uppercut from below the ground as a method of countering Neji's Byakugan; while Neji could have seen through the ground if he focused, his mind was instead focused on his 360 degree line of sight, which he had been using all battle long.
Rasengan Training - Due to his lack of talent in chakra molding, Naruto is seen as a having poor intelligence, but displayed creativity in using a Shadow Clone to assist in the stabilization of a Rasengan. This method, seen as a poor imitation, allowed Naruto to make a stronger form in the Odama Rasengan, and to accomplish what even the Fourth Hokage and Kakashi, both genius Shinobi, were unable to by combining nature manipulation to his Rasengan.
Kakuzu - Using a pair of Shadow Clones, which were easily dispatched, the real Naruto was able to judge the form by which the opponent fought, without causing any harm to his own body. This provided him with an estimate of the range that Kakuzu had with the tentacles sprouting from the masks on his body, giving him some clue as to how distant he needed to remain. He then created more Shadow Clones in order to use the new Rasengan without placing himself in danger. The outcome remains to be seen.