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> 病人を気遣って何が悪いののさ

is the sentence a friend sent me. The meaning is

> "What's wrong with worrying about a sick person?".

However, what do the trailing の's do and what is さ doing here? My professor
explained it briefly as being similar to ですよ but I don't understand why it is
being used here.

My only guess is that the first の is being used like it would be in this
example sentence:

> 赤いセータと青いのを買った = I bought a red sweater and a blue one.

and that the second one is being used as a question marker turning the さ into
a colloquial form of ですか
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grammar
What do all these の's do in this sentence?
病人を気遣って何が悪いののさ : "ののさ" is a typo as the comment had pointed out.

> 1) 病人を気遣って何が悪いのさ  
>  = 2) 病人を気遣って何が悪いのさ？  
>  = 3) 病人を気遣って何が悪いの(？)  
>  = 4) 病人を気遣って何が悪いのですか(？)  
>  Why not caring the sick?

1), 2), 3) are colloquial expressions.

※ There is no Japanese expression "何が悪いのですよ."
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EDIT: Downvotes indicate there may be some misunderstanding, so I added some
explanatory information below.

The "standard" use of 「～さ」as a sentence ending particle is common and well
known. [This
link](http://www.guidetojapanese.org/learn/grammar/sentence_ending) for a
quick lesson on it courtesy of Tae Kim.

However, the use of 「のさ」 at the end of a question is not common use with
standard Japanese. I asked a few Japanese people at work and they all did not
recognize this use. I did, however, get an answer from someone who is from Mie
prefecture.

「のさ」is a common auxiliary verb found in many [Japanese
dialects](https://ja.wikipedia.org/wiki/%E6%97%A5%E6%9C%AC%E8%AA%9E%E3%81%AE%E6%96%B9%E8%A8%80%E3%81%AE%E6%AF%94%E8%BC%83%E8%A1%A8)
used to emphasize the sentence, especially the verb. (Reference only in
Japanese, sorry. Could not find equivalent data in English.)

Think of it almost as an exclamation mark.
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answer
First of all, the sentence:

> 「病人{びょうにん}を気遣{きづか}って何{なに}が悪{わる}い **のの** さ。」

makes little sense as is because of the 「のの」 part. As has been stated by
others, that should be a single 「の」 instead.

Second of all, your professor's comment makes no sense if I may be honest.
That is if s/he is saying that 「ののさ」 or 「のさ」 means 「ですよ」.

The 「の」 in 「悪いのさ」 is a particle expressing affirmation/declaration.

The sentence-ending particle 「さ」, when used in conjunction with an
interrogative (in this case, 「何」), expresses a light kind of **_refutation_**.

> "What the heck's wrong with worrying about a sick person?"

By now, it should be clear (if I did an OK job here) that the 「の」 has
absolutely nothing to do with the 「の」 in 「赤{あか}いセータと青{あお}いのを買{か}った 。」. The 「の」
in that sentence is a nominalizer. "a blue **_one_** ".
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