Well, I don't really like comedies with Arnold.
When he is playing in a non-comedy movie, he has a "pinch" of auto-irony usually anyway, just enough to make his characters/acting more likeable.
But comedies seems to try to exploit this too hard, and the effect is not-so good.
Besides, he was never a good actor, and this is a part of the "magic" in the whole story.
A kid from Austrian village has a plan to be a movie star in Hollywood.
He is poor, and can't act, but has talent for bodybuilding, so he becomes world's best bodybuilder first, what allows him to move to USA where he slowly but steady starts performing in movies.
His English is so bad, that he is being dubbed in his first movies. but later his thick accent becomes a part of his trademark.
The rest is publicly known, he is the most successful body-builder-actor of all times.
After that he becomes governor of California, because why not?
Nothing is impossible for "Übermensch".