When filling out the Volunteer Recruiter Packet, what are some "show stoppers" to be aware of that can get the packet denied?

It's less in depth than a SECRET clearance is. You're not guarding nukes, you're recruiting. It's basically to see that you can handle your day to day life without any crazy stuff distracting you from the job. It's not like having $20k in unsecure debt will stop you from being a recruiter, or that being diagnosed with PTSD will stop it (depending on severity) - low and behold I had both and am sitting in USAREC right now.
If you can pass height/weight and APFT, don't have any bad NCOERs, and don't have any current open civil cases or are in collections, you'll be fine. Not only that, but once you're at the recruiting course you'll be blown away at a lot of the people "selected" and supposedly in the "top 10%" of their MOS.

Of course NCOERS. Plus if you are currently in a critical MOS. Plus some article 15's that reflect on you character.

Depends on type 1 or type 2 offenses. Also there are ways to dismiss those as well. 1 with type 2 5 years or older.
Type 1 is trickier and can be humbling. Have to go all the way up your chain and disclose your situation all the way up to people who dont know your case or background and an mfr to clear said charge or wasnt convicted just questioned etc... I have a couple contacts who have done this before if you like I can follow up with them for better guidance.