Send back a corrected case study?

Good idea 

Do others think it might be a good idea or am I risking something? I don't know if there is any particular process etiquette that I might not know about. 

Send a thank you note for sure.  If you've already done the work to correct it, you might as well attach it...it certainly can't hurt, and I think there are definitely people / teams out there that would appreciate you having been proactive in doing so. 

Only downside I could think of would be if they didn't catch the mistakes and you send something new to them that highlights it, but it sounds like you had a conversation specifically with the interviewer about them so I'm assuming that's not the case.

No, you already demonstrated you actually know the technicals underlying your mistakes and likely wouldn't make them in a real life environment (more than 2 hours). What if you make additional mistakes, or don't catch them all?

Did it for a case study. With the timing pressure, got my units confused (it was thousands not millions), and structured the deal much diffferently (i.e. bonds instead of term loan + mezz). The case study was a model that you sent within 3 hours, and a write up / deck on whether it was a good deal that you had to send 9 hours after the end of the model. Given how much a good deal is dependent on financing viability, I reworked the model and based my write up on the updated deal structuring. Can't say if it worked for sure but got moved to a final round (ended up declining but they followed up multiple times to get me to go to a super day). Unique situation with the case study obviously (not a one and done model), but think "correcting" the model ended up being appreciated. With that said, I thought I made a pretty unique write up with insights / thoughts that most people from M&A wouldn’t have been able to make, which might’ve been the differentiator.

I didn't have time to send the corrected case study, they told me that I got the position the next day after this thread! Thank you all for your valuable advice

Rule of thumb, if you find an error in your work just send the corrected version regardless. It may not (and likely won't) improve your candidacy but at least you're not signing off with wrong work material. I did this during one of my PE interviews and despite the tardiness in my correct model which I sent an hour after sending my original one which had a linking error in the LBO that caused the BS to not balance when changing assumptions, I got the final interview post-sending the corrected work. Now I'll never know whether it was because I sent a corrected model or what but at least I'll never have a doubt in my mind that I provided the firm with the best quality work I could provide..