To what extent has the Earth's surface been geologically mapped?
As far as I know there are no official data on this. All I can do is give a rough estimate, based upon work and personal interest in about 30 countries, over 40 years. 

We can say with certainty that everywhere has been mapped at the 1: million scale although, at this 'reconnaissance scale', at least half of the land surface is only sketchily known, with sparse ground-truth in areas covered by ice, dense forest or drifting sand. In such areas the best detail is probably from geophysics rather than from actual surface mapping.
For example, gravity anomaly by satellite, or aeromagnetics. 

At 1:100,000 scale most areas (I'm guessing 80 to 90%) are mapped wherever there is reasonable bedrock exposure. Certainly in Europe, the America's and most of the world's mountain chains you would be hard-pressed to find areas that haven't been mapped at this scale, although the maps are not all available ('commercial, in-confidence', etc.).
The only exception I can think of is parts of the less accessible Himalayas, where the scales of around 1/2 million seem to be the best on offer. That's not to say that there isn't much scope for further mapping at 1:100,000 scale. Rock exposure changes over time, and many of the existing maps could use a more detailed upgrade, especially in respect of microfossil zonation, facies zonation and structural analysis. 

1:10,000 scale or even finer detail is only for the 'very interesting' bits, such as ore deposits, mining tenements, reservoirs and engineering site investigations. There are thousands, if not millions of such maps, most of which are not publicly available. Your guess is as good as mine about what percentage of land is covered by such maps, but I would guess &lt;&lt;1%.


PS I forgot to add that most geology students and academics undertake geological mapping for thesis or teaching purposes. Again, they are often not published, and one has to search quite hard for a copy. These scales are usually somewhere between 1:10,000 and 1:100,000