There are a lot of things you can ask for that will red flag an organization as a whole.
Are you being given stock. Ask for a cap table and learn to read it.
Tell them your wiling to sign an NDA, and that you want to look at the repository. Tell them that you may need to ask follow up "who is who" questions to pin checkins. Code never lies. Embattled areas of code, and comments are great targets for your search.
Ask about recent outages and technical issues. Are they having problems keeping things up and running. Ask about how they were identified and how long to resolve.
Do they have documents for requirements? Wireframes, PRD's. Ask to see these as well.
If they raise any objection to any of this, just ask for a reason. It might set off an alarm for you. It might be reasonable.
Since you have some history with the other team leads, make a personal phone call. Start the call off that way (that its a personal call) and that you want to know the truth/history here because you have concerns. If there is something funny going on in the background one of them might just give you an honest answer.