It would be better to use
Code:
Dim dbs As DAO.Database
None of the other declarations are used. Why are they in the code?
Code:
Private Sub Update_Click()
Dim dbs As DAO.Database
Dim Passwords As Variant ' not used - no value assigned
Dim DateUpdated As Date ' not used - no value assigned
Dim ExpiredDate As Date ' not used - no value assigned
Dim loginID As String ' not used - no value assigned
Also, did you manually walk through the code?
Lets say my current password is "Password1" (yeah, I know - not so secure)
Step 1) Enter the old Password:
I enter "WordPass" into Me.OldPassword
Step 2) Enter the new Password:
I enter "ABC123" into Me.NewPassword
Step 3) Re-enter the new Password
I enter "DEF456" into Me.ConfirmPassword
Step 4) Update the password.
Nowhere in your code did you check to see if the value in Me.OldPassword matches the current value for the password. If the old password doesn't match the entered password, shouldn't the password update be canceled?
Neither did you check to see if Me.NewPassword matched Me.ConfirmPassword. If Me.NewPassword doesn't match Me.ConfirmPassword, shouldn't the update also fail?
You just check to ensure that three values have been entered, then update the password. 
Maybe you might want to rethink this bit of code??? 
Not trying to tear you down..... you did ask for advice. These are the problems that jumped out at me.