Many GRT inconsistencies are well-known:
1) the principle of correspondence is violated (the limiting transition to the case without gravitation cannot exist without introducing the artificial external conditions);
2) the conservation laws are absent;
3) the relativity of accelerations contradicts the experimental facts (rotating liquids under space conditions have the shape of ellipsoids, whereas non-rotating ones - the spherical shape);
4) the singular solutions exist.
(Usually, any theory is considered to be inapplicable in similar cases, but GRT for saving its "universal character" begins to construct fantastic pictures, such as black holes, Big Bang, etc.).