What are the threats posed by this situation?
Threats include information leakage as this info could be in your logs in plaintext:
- Passwords for other sites or systems.
- Partially entered passwords for your system.
- Old, similar passwords.
- Old passwords that were attempted since password was changed, which may have been reused elsewhere.
- Passwords with typos for your system.
All stored along with the name of the user account.
Anyone with access (all team members in your case) will be able to read these entries, and if not properly secured the consequences could be worse (as normally passwords should be stored salted and hashed using a slow algorithm to guard against situations where the data is accidentally leaked).
Should we notify users about that or just remove entries from logs and move on (those were invalid passwords after all)?
Definitely. You should inform all users that they need to change their password ASAP. If your system has any password reset functionality then you should use this to temporarily disable all accounts until their password has been changed (details of how to do this depends on the sensitivity of your system - e.g. whether password resets via emailed short term links with random tokens are acceptable).
How can I convince decision-makers to make the right choice?
Explain that unless the company is 100% sure that the log files have not been leaked in any way (either hacked or by an employee on purpose or accidentally), then all accounts are at risk unless passwords are changed.