Commercial planes don't do much with GPS. Flight systems are slaved to the Inertial Navigation System.
> If you enter in 01 but end up on 10, the plane should be able to figure out it's pointing the wrong way and is in the wrong place.
Another sibling post already talks about this.
Note that the only thing the plane can do is to warn.
Citation needed. Which planes? Can you even take off without configuring your INS? Are the instruments slaved to the GPS system now?
On some jets there is an annunciation system(RAAS) that also yells at the pilot all the time saying where he is... even in the sky. For instance, as he's about to land, it yells "approaching 28R", or on the ground, "on rwy 28R"
So the tech exists. The challenge is that there are a lot of older planes flying around, tech in that highly-regulated environment is slow-moving, etc.
And for the punching in the wrong weight, the system should be able to determine weight from acceleration dynamics and issue a warning as soon as the plane moves.