The Pacific Ocean is very big, and very empty. 1930's navigational tools were primarily a map, compass, and watch.
It would have been very easy for even a highly skilled navigator to miss a small island in a very large ocean.
As recently as the late '60s, navigation in that part of the world was exceptionally difficult. In the late '60s, one of our Navy ships rammed a reef at flank speed because the navigator thought he was somewhere else and thought the breaking waves were caused by a tsunami. Proper procedure when encountering a tsunami was to attack it from a perpendicular entry at top speed.
Charts were not always that accurate and navigational tools were limited to sextant, LORAN-C, Omega, and dead reckoning.
Accuracy of LORAN diminished to the point of non-existence with distance from the master/slave stations.
Omega was a low frequency device that was technically international and provided good replication. In other words, it would tell you that you were in the same place whenever you were in that place--but it wasn't necessarily where you actually were. It was common on submarines bacause the ultra low frequency radio waves could actually penetrate the water allowing the sub to get a position fix without surfacing. It was also commonly used on long distance flights. But it was commissioned in 1971 and didn't exist when AE was flying.
Navigating with a sextant could provide reasonably good fixes a couple of times in a 24 hour period, but was dependent on sea state and cloud coverage--and you can get pretty lost between fixes. If it was bad overcast, you couldn't even get a local apparent noon sighting to give you a longitude. Shooting the stars at night would give you a proper fix, but was also limited by cloud cover and sea state. Pilots also used sextants when traversing long distances. Another factor leading to inaccuracy; it was easy to mess up the math when doing sight reductions from the tables. That may be what happened to AE.
Dead reckoning is simply plotting your observed compass/gyro course using time and speed to find distance. Navigators try to account for set and drift (the effect of wind and currents on true course) but that's pretty much a by-guess-and-by-gosh sort of factor.
It wasn't until the mid-'70s that Sat-Nav came into being. It had accuracy to within 9 meters, but required one of the satellites to be at the proper angle to get a fix. The satellites formed a birdcage surrounding the earth, but there were initially only 7 of them, so there were holes in coverage. They were in a polar orbit, and it could be as much a 13 hours or more between satellite fixes when your ship was near the equator.
Of course, everything changed in the mid to late '70s when GPS was introduced. Military units can provide one meter accuracy in lat,lon,altitude at MACH One. When stationary, accuracy is increased to centimeters.
It's all a definitely interesting mystery.
Crusader Rabbit