- what is the license? (Avoiding copyleft headaches)
- do the issues look cared for?
- is there an issue asking “is the project maintained any longer?”
- what business or person is behind the project? What is their motive for creating the project?
- how much of an impact would it be if the project disappeared tomorrow? Could I maintain a fork or rebuild it? Is it core business functionality or a side thing?
- do others at my company use it? Or do they have a different library/etc for solving the problem?
For example, there's a library we rely on for our product where they put an intern in charge of issues and take 5 months to accept pull requests or fix the bug. This has lead us to develop plugins instead of contributing or maintaining a fork (not to deal with conflicts).
If your app is server-side, GPL explicitly permits "private use" of GPL code without licensing anything to anyone, as long as you keep it private on your server.
I have never had the need (nor was I asked) to vet code in depth before adding a dependency.
Even if you're not actually running your code on Debian / RHEL / whatever, using libraries that are distributed by those vendors where possible is a good start.