lol @ the plane one. In theory I suppose they are right, if the plane was flying at an exact straight line, and assuming the engines were actually powerful enough and had their own oxidizer and that it was flying at a faster speed, then yeah. But in the real world, pilots actually ARE adjusting the plane into a curve (not actually dropping their altitude though!), typically flying towards a certain point relative to horizon, which is technically going to create a curve over a long distance.
As for gyro it would be interesting to set one on a large sphere that turns very slowly. I'm pretty sure there is a certain point where a gyro is going to not be affected by movement because the movement it is getting is so small that it won't "notice". Same idea if you pull a table cloth really slowly, what's on it will move with it. If you pull it fast, it will stay in place.
On similar note, that whole thing where toilets flush another way or stuff drains the other way in the southern hemisphere actually has as science to it. If you have a very still body of water and a drain, it will drain the other way because the rotation of the earth affects it. As for toilets typically the design will overpower that effect though so it will flush whatever way the water is released in the bowl.