When I try to log into my brokerage account and allow Safari 10 to autofill the password, it consistently enters the wrong password. Safari > Preferences > Passwords has the correct one but I always have to type it in manually rather than use autofill.

I have deleted that site and password info from the preference pane and re-entered it manually (Safari asks if I want to always allow, and I agree) but the next time that I try to log in, the same thing happens. I have also cleared Safari caches, to no effect. This does not happen with any other website. This behavior is not new with Safari 10; it happened in Safari 9 as well.

How can I make Safari autofill the correct password?

An off-the-wall thought, but maybe the brokerage site no longer accepts auto-fill passwords. Perhaps it wants to make sure you are you.

Nice thought, but I don't think that's it. Safari does autofill a password, but it's the wrong one.

Have you tried deleting the entry for the site in Keychain?

I tried this at your suggestion and now it just offers to suggest a password. When I typed in the actual password, logged in/out and tried to log in again, the same thing happened. BTW, when I try to have Keychain Access show the password, all I get is dots (6, although the password is actually 9 characters). KA shows my password for other sites so this may be a security feature with this site. The same thing now appears to be happening with Safari > Preferences > Passwords.

Reinstalling Safari 10 may be an option, but if you haven't got the installer archived there's no way I'm aware of to do it.

Maybe try deleting the site from Safari > Preferences > Passwords and shutting down/starting up before trying the site again.

As I said in my first post, the problem existed in Safari 9, so I doubt that reinstalling Safari 10 would work. I tried your second suggestion (deleted that site from Passwords and actually restarted the computer rather than just restart Safari). After successfully logging in, I logged out and tried to log in again. The password that Safari entered (from my stored passwords) was again the incorrect one. It will not display in either Passwords or Keychain access (I just see dots).

This is a relatively minor issue but I'd like to solve it if possible.

EDIT: Apparently, the problem somehow lies with how Safari sees the site. I tried this in Firefox (which I rarely use) and the correct password was remembered. (I have a FF extension that allows this.)

It sounds like you have multiple entries for your brokerage login stored in Safari. [I've had similar happen to me in Firefox after a site changed subtly and required a renewed login; both logins were saved, rather than one replacing the other.]
I don't know squat about Safari 9 or 10, but if they're anything like Firefox you can examine "Saved Logins", delete your brokerage login which would also delete its password — making sure that you don't have multiple entries for your brokerage login — and then re-access the site, permitting the login to be saved.
If this is the way Safari 9/10 works, then all should be good.
If it isn't, then your brokerage site is at fault, not Safari (or so 'twould seem to me).

AFAIK, Safari has nothing like that Firefox feature. I'm inclined to agree that the site is at fault.

More info: I have an account with our local library. The login ID is my account number but the box to enter it doesn't say "login" or "user ID". Instead, it says "library account login." Safari will remember the password but not the login. Firefox, on the other hand, has no problem with either.

Out of curiosity, is the incorrect password an "out of the blue" item or is it one you use?

Edit: I believe it was you who once posted a means to make Safari entered passwords visible.

I just looked at my Safari 5 and under Preferences > AutoFill found that one should be able to "Autofill web forms" with user names and passwords.
(1) Is this not a feature of Safari 9 and 10?
(2) Would this not be the equivalent of Saved Logins under Privacy in Firefox?
(3) Or did I miss something in translation?

The incorrect password is an old one that I once used but changed. It is very easy to make entered passwords visible by hovering the mouse over the password field and pressing Command. This works with virtually all sites except the problem one in question.

On second thought, I'm not sure if the incorrect password is the old one. First of all, the technique of hovering the mouse and pressing Command doesn't show it. Second, it's six dots, indicating six characters, and I would have made it at least 8 characters.

1. You are correct.
2. I don't know the answer since I rarely use FF, but it sounds about right.
3. ¿Quién sabe?

And so it still doesn't work for you?

Nope, it doesn't work.

I don't think the number of dots is indicative.

I've run across any number of instances in which the number of dots I've seen has had nothing to do with the number of characters in my password; I imagine that it's a "diversionary" tactic to throw off potential bad guys.

safari fetches passwords from its forms autofill database. In Safari, go to preferences, passwords. Find and DELETE the offending entry. QUIT SAFARI. Relaunch it. Check it again. You may find it again when it didn't show up after delete. If so, delete it again. Repeat until safari truly has forgotten it.

keychain access and apple remote desktop both have problems with getting duplicate entries into their heads, where it shows you the first entry (only) and uses the second. So you have to delete it. quit. relaunch. delete AGAIN. (sometimes more than once)

You are absolutely correct! The number of dots Apple shows in the password field has ALWAYS lied since the first OS X public beta and maybe even before then. I remember a fair amount of comment/complaint about this on MacFixIt about this back in the day.

The idea is to prevent someone lurking over your shoulder when you are entering the password and getting the correct number of characters, thus making guessing the password that much easier. With today's brute force password attacks it probably doesn't reduce the risk that much, but every little bit helps.

There are also a number of apps I've seen show me only dots when I go into prefs to check something like its server connection, and notice there are more or less dots than I usually see (~10) "by default". Then I notice the number of dots matches the length of my password.

And then I say, "Ooooo I learned something today!" That almost certainly means that the app is storing the password in some "recoverable format", rather than as a hash. (anything you hash will turn into a string of garbage of the same length as every other hash) So when you see that, consider your information less secure, because a bored hacker can extract your password from that app. There may as well be a "Show Password" checkbox off to the right. (and I see that occasionally)

Apps should show dots a you enter a password, and then when you go back to review the settings, the password field should be some fixed number of dots.

I've even encountered a few apps that let me EDIT a saved password, while in dot form - "ok this password ended in a 7 or an 8... ok 7 didn't work, delete last dot, change to 8... ok that worked." If you try to edit the dots, as soon as you do anything, the field should clear and you are starting from nothing, because you can't edit a hashed password.

I assume that your password is pretty long, because otherwise it's liable to have the same number of characters as the number of dots, but only coincidentally.