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If the earth was considered a point in a problem, it is because it simplifies calculations and the effect is exactly the same, or the difference is insignificant.
Solids of any size can be considered as a point in certain physics problems. For the purpose of the attraction of gravity between two homogeneous spherical objects, for example, each object can be considered as a point with all its mass concentrated on its center. For the purpose, the effect of gravity is exactly the same.
On the other hand, in problems involving short distance movements on (or slightly above) the surface of the earth, the earth is considered flat/horizontal with gravity pulling in parallel (vertical downwards) directions. We do not even want to consider the curvature of the earth in those cases, because it does not make much of a difference.
For large distances, the curvature of the earth matters, and when traveling around the earth at high enough speed (or with precise enough watches) we may have to consider relativity.