are there any interactions that only happen when you input the correct password on day 3?
I hope this isn't too vague to answer, I don't know how well known the password is and I don't wanna spoil what it does.
Nope! That's really just a developer cheat code. It won't be in-game in the final release probably.
Would be a neat easter egg to have in the release but I wouldn't miss it much if it was removed.