Also, I think the vast differences being referred to would the fact that if you were to take a known distance on the RE map or globe from point A on one continent to point B on another, then randomly select another transoceanic segment on the opposite side of the map especially south of the equator, you have 2 known lengths of travel right?
Well now, 'flatten out' the earth, reconfigure it however you like, and odds are - unless you totally mess with the orientation of the continents, the measurements don't work out the same. Not to mention if you move the continents around to make up for it, then all your other measurements are off now.
So in effect - it really isn't possible for the measurements from one continental location to another (if that far) to work out on a flat map. It is especially noticeable 'south' of the equator.
Anyway, gotta git down the road here - sorry if I missed something or didn't word that well enough. Gotta go!! 
Take it easy,
John
And where would such possibly minor distances errors be accurately noted?
I'm not sure I understand your question ... do you mean where would short distance errors would occur? Or that anything I mentioned would be a minor distance error?
I will assume the latter. I'm trying to think of a better way to describe it for you. I hate to use an analogy here but I can't think of a better way to do it... to simplify this experiment take a cylinder (or globe if you want, that's fine too) and place upon it a couple of Styrofoam blocks or shapes of some kind.. relatively thin is fine and glue them down good and tight. place them relatively close even.. the more so the better to prove the point. Farther away and it will be more of an effect, but this shows the minor differences you were pointing out also.
Now stab a pencil or needle or what have you into each block wherever you choose, string a thread tight between them, then cut the cylinder along the backside, and lay it out flat. You will notice that the thread now droops. This would be an example of a northern discrepancy between known current distance between two points and if you were to flatten out the earth.
For the south pole, all you have to do is reverse the concept, cut the cylinder from the front and the thread either springs tight trying to keep it together or snaps.
Hope that helps, if not let me know... I'll try to do better.
Take care,
John
Edit: Also, in case the last part doesn't seem feasible, take a circle or disk, wrap it into even a gentle cone and repeat the same experiment, attempting to flatten the cone back out into a disk... the string will tighten out or snap sue to the distortion.
Before anyone says this proves nothing but experimental shapes, these are only experiments to prove distance variances - take into account we ALL know how far it is from say Tokyo to LA, or in common discussion here; say San Francisco, CA to Sydney, Australia - 7408 miles (11922 km) (6438 nautical miles) [a long haul I make at least once a year to see my brother... ugh!]
Take care,
John