Maybe the world really is flat?

Nah. Easy way to see this is to derive (or look up) the expressions for the gravitational potential due to a sphere and due to a uniform plane. Then, fit the actual gravitational potential using known weights and simple gear to the same nonlinearities found in the two derivations. The spherical expression should be a much closer match. My college physics course actually had a unit where we fit the gravitational potential, so it’s extremely technically easy to do.

Also, airliners fly long haul flights in patterns that “look curved” on any flat map. This is because topologically speaking, a flat plane surface has one global chart, whereas there is no global chart for the sphere, so any chart map will distort the true distances compared to the original sphere. (The neat thing about the theory of manifolds is that all these words have technical mathematical definitions that basically line up with their plain English usage.) This shows that, at least when it comes to flying airplanes, i.e. what ways you are allowed to traverse the sphere, the Earth is topologically equivalent to a sphere.

the moon landing

Also nah.

wtop.com/…/the-experiment-still-running-on-the-mo…

This one is harder to demonstrate without a bit of money.

But also…if it never happened, why would the Soviet Union have let the government win the Space Race? There was enough historical and scientific evidence at the time for all world powers to conclude that it must have happened.