(没)有什么好X的: nothing to X, what is there to X?
【四69】口语格式 / fixed patterns
Tone colorsā tone 1á tone 2ǎ tone 3à tone 4a neutral
没有什么好 + V + 的 says that nothing deserves the action V: 没有什么好担心的, “there's nothing to worry about”. Its question form 有什么好 + V + 的? is rhetorical, “what is there to…?”, meaning nothing. 好 here means “worth, fit to”, and the final 的 is part of the pattern; it can't be dropped.
The verb is usually a feeling or a judgement: 担心, 害怕, 紧张, 生气, 笑, 看, 说. You reassure (没有什么好怕的) or brush someone off (有什么好说的？). Like any rhetorical question with a question word, it never takes 吗.
Compare 不用担心 (“no need to worry”, a plain permission): 没有什么好担心的 judges that nothing justifies the worry. Spoken register, with the same disguised negation as other rhetorical questions such as 怎么会……呢？
Examples
别紧张，没有什么好担心的。
Bié jǐnzhāng, méiyǒu shénme hǎo dānxīn de.Don't be nervous, there's nothing to worry about.
这个地方没有什么好看的。
Zhège dìfang méiyǒu shénme hǎo kàn de.There's nothing worth seeing in this place.
这有什么好笑的？
Zhè yǒu shénme hǎo xiào de?What's so funny about that?
你已经准备得这么好了，有什么好担心的？
Nǐ yǐjīng zhǔnbèi de zhème hǎo le, yǒu shénme hǎo dānxīn de?You've prepared so well, so what is there to worry about?
这么小的事，没有什么好说的。
Zhème xiǎo de shì, méiyǒu shénme hǎo shuō de.It's such a small matter, there's nothing to say about it.
你又没做错事，有什么好害怕的？
Nǐ yòu méi zuò cuò shì, yǒu shénme hǎo hàipà de?You haven't done anything wrong, so what is there to be afraid of?
Common mistakes
✗ 没有什么好担心 → ✓ 没有什么好担心的 (the pattern ends in 的).
✗ 有什么好担心的吗？ → ✓ 有什么好担心的？ (a question-word question never takes 吗).