Somewhat relevant: the island of New Guinea was certainly charted and colonized. But up until 1930 the inside of the island were considered completely uninhabited.

In reality there the valleys and highlands were heavily populated. That was only discovered when the territory was first overflown by an aircraft.

Three expeditions leaded by Richard Archbold from 1933 to 1939 explored to inside of the island and put in contact the native populations with the rest of the world for the first time in centuries.

Its not likely at all that an island of that size would remain unfound in 1933, mysterious perma-fogs would help, but then people would have noticed and investigated the fogs. Certainly smaller island could have, theoretically, primarily at low latitudes. However there had been significant coverage of the entire surface, especially by marine powers like Britain, France and the US. Whaling and Sealing ships were pretty efficient in their search for prey though and they covered a lot of ground. IF anywhere was goign to hide an island it would be between New Zealand and South America and close to the Antarctic, but not too close.

Even some of the most remote islands, the Kerguelens, were found way back in 1772. Bouvet Island, the most remote island in the world was found in 1739. Those blokes in old sailing vessels were amazing.

However its hard to prove a negative. If we hadnt found Island X in 1933 we wouldnt have know we hadnt found it. Its certainly plausible that an island somewhere remained undiscovered, just nothing of the nature of the movie one. I suspect it was entirely plausible to the audience at the time, but then its probably plausible to some today.

There are still areas of the sea that haven't been surveyed, but rather unlikely that entire islands have yet to be discovered. On the other hand, whilst sailing around the Bismark Archipelago, there were islands marked on the Admiralty Charts "reported to lie 20 miles North East of this position", and "The existence of this island is doubtful". That was in the early 1980's, which would suggest that these regions still hadn't been properly surveyed. Essentially, the reason would be that these areas, rather like the area to the South and East of the Spratly islands in the South China Sea, in that it would be most unlikely for European or American, for example, commercial vessels or naval vessels to need or want to navigate those waters, so there would be no need for any of the maritime powers to use the enormous amounts of resources necessary to thoroughly survey the areas.

The 1930s were a scientifically-fascinated decade. Popular scientific magazines routinely sold out, and science-based heroes were the biggest draw at the news stand (Doc Savage Magazine had a circulation of between one hundred and five hundred thousand, month in and month out). Travelogs were the second most popular of theatrical short subjects, and inspired sometimes fanatical devotion.

But, more than that, the era had a fascination for adventure yarns. The fact that much of the world had been mapped did not reduce this fascination: Tarzan existed in an area of Africa that was, on the whole, fully explored; there's a great deal of Tom Foolery in Lost Horizons to explain away why Shangri-La should exist in an otherwise known part of Tibet.

The lost world setting existed to promote verisimilitude, and give the creators leeway to do as they pleased without depending on the public's knowledge of real world places.

My figures are drawn from Rick Lai's The Revised Complete Chronology of Bronze and William Patrick Murray's longform series of Doc Savage analysis from Nostalgia Venture's Doc Savage series. The reference for Tarzan's location, and it's heavily populated real-world situation, comes from Philip Jose Farmer's excellent Tarzan Alive. Lai and Murray references the same theory that such places were to increase verisimilitude and give authorial freedom (as well as to allow social commentary which would otherwise fall on deaf ears).