Warning: This list contains spoilers for all the Indiana Jones movies, including Indiana Jones and the Dial of Destiny.
On its own, the skull has some psychic abilities if a person looks into its eyes for too long. Oxley also uses it to divert an army of red ants away from himself and Indy. Additionally, the skull has a very strong magnetism, attracting metals that aren't even magnetic. However, other than these incidental properties, the crystal skull is not that powerful in its own right. The issue is that all the real power the skull has is attached to the alien race it comes from.
The loss of the stone causes a blight of drought, crops failing, and livestock dying in the village. Indy causes the stones to burn by reciting a Sanskrit incantation during the final fight. When Indy returns the stone in the final scene, Mayapore's bountiful crops and water have apparently returned. Mola Ram also believes that if he could find all five stones, he could rule the world.
The barrage of defenses surrounding the Holy Grail also demonstrates its power. When Donovan drinks from the wrong goblet, he immediately withers until he turns to dust. When Elsa attempts to leave with the real Grail, the entire temple begins to collapse. Traps surrounding an artifact are characteristic of an Indiana Jones adventure. In the case of the Grail, they are not indisputable evidence of its power, because it's not clear if they are directly triggered by the Grail itself.
Related Indiana Jones And The Dial Of Destiny: 31 Easter Eggs & Hidden References Indiana Jones 5 honors the entire legacy of the adventuring archaeologist with several fun Dial of Destiny Easter eggs and references. 1 The Ark Of The Covenant Raiders Of The Lost Ark Close The way the characters speak of the Ark creates an image of it that is too powerful for any person to understand, let alone be able to use that power for themselves.