An important feature to include is when logging into a website, there should either be a statement about the password policy or a tool-tip like thing to hover the cursor over to reveal the password requirements.
Sometimes when I'm in a rush to register on a site, I'll use a quick variation of a common inexpensive password I keep in my head, and I'll modify it to fit the password policy that site is enforcing. I'll then neglect to make a note of that registration in my password manager (if I were going to use the password manager, I suppose I'd have it generate my password anyway). When returning to the site later, having forgotten my registration, I'll try one that makes sense based on what I would have done for that site, but I'll get incorrect password errors.
It would be really nice, even if only after a first failed password attempt, for the site to tell me, "Hey, your password is wrong. It should be 8-40 alphanumeric characters, no hyphens or any other silliness." So that I'm not trying otherwise strong passwords that don't make any sense for that site.
Furthermore, when a site states a password policy while registering, it should darn well enforce the policy it states. It frustrating when it says certain characters are (dis)allowed and then proceeds to enforce some other hidden policy.
Edit: P.S. Also, please please don't truncate my password and then not tell me about it! It's ever so much fun when my password is shortened at registration by the form's character limit and then a different (longer) limit is encountered on the log in page and suddenly I don't have the correct password anymore