I Corrected Someone's Use of Commas and Now I Don't Know if I Was Right

I prefer your version of the sentence: Comedy today is dead, murdered by political correctness.

If, however, a person chose to pause after comedy and is, that would be quite OK, as in the following sentence:

Mr. Kitchener, presumably, was responsible for the mishap. [Granted, the construction and parsing of this sentence are a bit different from your original sentence.]

Speaking more quickly, that sentence becomes this sentence:

Mr. Kitchener presumably was responsible for the mishap. [In speaking the sentence quickly, there would be no need for commas.]

As for your second question about where the period in your parenthetical remark goes, the period could logically go inside the parenthesis, before or after the quotation mark, as in the following:

(I thought they made "today" an appositive of "comedy.")

(I thought they made "today" an appositive of "comedy".)

Since you are not quoting yourself when you include the word comedy in quotation marks, I think putting the period after comedy would be the way to go. If, however, you were quoting someone within your parentheses, the period would go inside the quotation mark, as in

(I suggest, by the way, that Lincoln was correct when he said, "You cannot fool all of the people all the time.")

Comedy, today, is dead; murdered by political correctness.

The commas surrounding "today" are correct. You can also move the "today" to the front of the sentence if comedy specifically died today. However, the semicolon is incorrect. As you wrote, "murdered by political correctness" isn't an independent clause (in fact, it isn't a clause at all because it has no subject).

Comedy today is dead, murdered by political correctness.

The lack of commas surrounding today is incorrect. "Today" in an interrupter, so it needs to have a comma before it and another after. The comma is correct, but you can instead use an em dash ("—") to add more emphasis to "murdered by political correctness."

Therefore, you have a few options (assuming you want to keep "today," which can be removed because it is an interrupter):

Comedy, today, is dead; it has been [or was] murdered by political correctness.

"It was" makes the part following the semicolon an independent clause, which makes the semicolon correct.

Comedy, today, is dead, murdered by political correctness.

This looks a little awkward and should probably be avoided.

Today, comedy is dead, murdered by political correctness.

This makes the above sentence more natural.

Comedy, today, is dead—murdered by political correctness.

The em dash instead of the comma makes the sentence more readable, even though they are essentially the same. The em dash also draws more attention to the last part of the sentence. This is, in my opinion, the best option.

Today, comedy is dead—murdered by political correctness.

This is, in my opinion, the best option (if comedy died today, specifically).

Today, comedy is dead; it has been [or was] murdered by political correctness.

This is also a pretty good option, depending on how much emphasis you want to place on the last part.

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Note: the sentences that start with "today" suggest that comedy died today (specifically). I would only use those if comedy died on the day when you are speaking. There also might be slightly different variations of these sentences that I forgot, but I think I wrote (almost) all of them.