While in Meteor Form, Minior cannot be afflicted by status conditions or become drowsy due to Yawn. Rest will fail when used by Minior in Meteor Form. If Core Form Minior is switched in while grounded (due to Iron Ball, Gravity, or being Baton Passed Ingrain), it will be poisoned by Toxic Spikes before Shields Down switches it to Meteor Form.
Role Play, Gastro Acid, Worry Seed, Simple Beam, and Entrainment fail if the target has the Ability Shields Down. Skill Swap fails if either Pokémon has Shields Down. Shields Down cannot be copied by Trace, Power of Alchemy, or Receiver. Shields Down cannot be replaced by Mummy or suppressed by Core Enforcer.
Mold Breaker, Turboblaze, and Teravolt have no effect on Shields Down.
From what I understand, Shields Down protects Minior from all status conditions. Shields Down also prevents itself from being ignored by a Pokemon with Mold Breaker; Turboblaze; and Teravolt, changed by a Pokemon using Simple Beam; Entrainment; or Worry Seed on Minior and making contact with a Pokemon with Mummy, being removed by Gastro Acid or Core Enforcer, and being copied by a Pokemon with Trace; Power of Alchemy; or Receiver.