I was reading a cartoon and the punchline is
The sentence just doesn’t sound right for some reason. Maybe because it’s using both him and his in a short span.
It’s a cartoon so I can see where you couldn’t really rephrase it and still get a joke out of it. And it probably would be better to rewrite the sentence, if it were in a book or something, but I was just wondering about the grammar aspect to it
shrugs. I don’t know what to say; it sounds fine to me.
The pronouns are correct. I would add a comma after “Well”.
Agreed. Otherwise, there is nothing grammatically wrong.
And a period after “his.” 
But I agree that these sentences are grammatically correct. We’re obviously missing the information and context that would make them sensible (or not), but there’s no problem with the grammar.
Maybe a period at the end, too. Otherwise, I see no issue. Having separate sentences is not even a problem: you could have a colon or semicolon separating the two and it would still be okay.
I was also going to recommend adding a period after “his”, but I remembered that in American comic book style, the final sentence in a word balloon is left without a period, although question marks and exclamation marks are used.
I would reword the first sentence to read: “Well, don’t expect his approval.” Just sounds better to me.
Would it feel better if we changed the pronouns? We can make it where “he” is the person talking.
“Well, don’t expect me to approve. Those are your values, not mine.”
I agree, I think it was the fact the words “him” and “his” were used so close together that through me off
Thanks
Give him his watch - does that also sound wrong to you?