English Translation
He hit my arm.
Would using “mich” here be a mistake? And perhaps replacing “den” with “dem”?
It’s just the idiomatic way of talking about body parts.
You can read more about this here: Ich habe mir den Fuß verletzt
The dative in this kind of sentence expresses what “someone does to or for someone”.
So in this example you can think of it literally as “What he has done to me is hit my arm.”
Yes, you could use “mich”, but you need to put it differently:
Er hat mich am Arm getroffen.
But that has a different meaning. The english “hit” here is ambiguous and doesn’t tell whether the intention was to “beat” (schlagen) the arm or not. My suggestion above makes it clear that “he hit me”, and the spot that ended up being hit was the arm - maybe even with a projectile.
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