It's a rule that minions suffer the worst possible result with a missed save (simple case, any failed Toughness save renders a minion dead or unconscious). Does this include Limited Degree with Affliction? And does the answer differ whether your Limited Degree is "No third degree" or "Only third degree"? I would think that if the former is the case, you'd probably have to decide what the third degree is against minions even though it would only come up with them.
It's the former. As the Hero's Handbook states (page 193):
If a minion fails a resistance check, the minion suffers the worst degree of the effect.
With any Affliction power, the worst degree is the most severe possible effect. Oddly enough, according to the Mental Powers power profile, "only third degree" is actually a valid flaw, and failing with one or two degrees still counts as failing. So yes, you can have a hero who's great at taking out minions, but is otherwise unreliable versus enemies with decent defenses.
One application of Limited Degree means there are two possible degrees of effect. With Extra Condition, this could mean multiple effects. If the minion fails the resistance roll, regardless of their degree of failure, they suffer the most severe effect(s).
Similarly, two applications of Limited Degree means there's one possible degree of effect(s). If the minion fails the resistance roll, then they suffer that effect / those effects.