According to all respective Bulbapedia articles on these moves, basically Wonder Guard and any ability which would affect the target's form is incapable of being copied, for example, Schooling (Wishiwashi), Flower Gift (Cherrim) or Illusion (Zoroark). It would also be very hard to Gastro Acid a Magic Bounce Pokemon, but apparently it's possible. Durant can give Truant to something else, but you can't change Slaking's ability with it; at one time, you could Skill Swap Slaking's ability, but I don't know if that's still possible. A full list of these can be found on any of these moves' Bulbapedia article.
Gastro Acid fails if the target's Ability is Multitype, Stance Change, Schooling, Comatose, Shields Down, Disguise, RKS System, Battle Bond, or Power Construct.
Skill Swap fails if either Pokémon has the Ability Wonder Guard, Multitype, Illusion, Stance Change, Schooling, Comatose, Shields Down, Disguise, RKS System, Battle Bond or Power Construct. Skill Swap works when both abilities are the same, but the only time something like that would be useful would be if they had something like Intimidate, etc.
Trace cannot copy Trace, Forecast, Flower Gift, Multitype, Illusion, Zen Mode, Imposter, Stance Change, Power of Alchemy, Receiver, Schooling, Comatose, Shields Down, Disguise, RKS System, Battle Bond or Power Construct.
Role Play fails if the target's Ability is Trace, Wonder Guard, Forecast, Flower Gift, Multitype, Illusion, Zen Mode, Imposter, Stance Change, Power of Alchemy, Receiver, Schooling, Comatose, Shields Down, Disguise, RKS System, or Battle Bond. It also fails if the abilities match.
Entrainment is a little weird. It would fail if it were hacked onto a Pokemon with Trace, Forecast, Flower Gift, Zen Mode, Illusion, Imposter, Power of Alchemy, Receiver, Disguise or Power Construct. I don't think any of them can learn Entrainment, because it would be inherently pointless.
Entrainment cannot change a target's Truant, Multitype, Stance Change, Schooling, Comatose, Shields Down, Disguise, RKS System, or Battle Bond.
