I watched "Tora, Tora, Tora," on Netflix over the weekend, and came away with this question.
At one point in the film, a flying instructor and student are flying and end up encountering an entire squadron of Japanese planes.
With hundreds of Japanese planes heading across the island, and people knew that hostilities with the Japanese were likely, how come no one notified officials at Pearl Harbor?
So the event portrayed did not occur in the backwoods of the island but near Pearl itself, the instructor named Cornelia Fort, landed at what is today Honolulu International Airport, so by the time she saw the planes they were already over Pearl.
The other consideration is that it doesn't take very long to pass over the island, just a few minutes from crossing the shore to when the attack runs began, and over the central valley and Western shore which are much less populated than the Eastern and Southern portions.
This is also of course besides the Army Radar post that did notice the large radar contacts but who were not fully operational and whose report was initially taken to be the flight of B-17's from California.
To add to some /u/DBHT14 answers here, one important facet of the Pearl Harbor attacks that their cinematic dramatizations often gloss over is that the attack took place relatively early in the morning. The Opana radar station picked up the first wave heading to the island at 0702 and relayed the information to the Fort Shafter Information Center but because of the hour, neither the Information Center's controller nor the aircraft identification officer were available. Lieutenant Kermit Tyler, the senior officer available, possessed neither the training nor the knowledge to correctly interpret the data coming in from Opana, so Tyler made the judgement call that the sighting was the B-17 flight from the West Coast (this mistake was also the result of the undertrained radar operator not telling Tyler that the signal was more than fifty planes). By 0740, the first wave had reached Oahu and Fuchida had given the signal to attack and the attack commenced at approximately 0753.
So when coupled with the early morning and the incredible speed with which the attack occurred after the radar sighting, it is perhaps understandable that the Japanese managed to achieve surprise. As for civilian spotting of the attack waves, there really was not a mechanism to report any sightings directly to officials in the island that mattered. Postwar testimony given to the Joint Session of Congress investigation of the attack noted that untrained civilian reports was much more of a hindrance to the correct dissemination of intelligence and the various panics on the West Coast in the months after Pearl Harbor bore this contention out. The existing Information Center, modeled on the British networks deployed during the Battle of Britain, on 7 December itself was only incompletely tested and understaffed. The Opana operator only picked up the signal of the attack because he wanted some extra training time on the radar, otherwise he would have left with his shift. Had the network been properly staffed, it was much less likely that the Japanese would have achieved the level of surprise that they did. While a proper alert would not have prevented the attack, it might have enabled the Army planes to disperse, man AA guns, and some pursuit planes to scramble. More importantly, it would have given the Americans a better idea of where the attack came from, so Halsey's carriers would not have gone on a wild goose chase in the attack's aftermath.