I don't have specific examples (sites), but I will make a note of them from now on. This occurs on many web sites, though.
I'll arrive at a page where I have created a login and saved it in LP, and I select Autofill. However if there are any other form fields on the page LP fills those instead of the correct ones. A common example is a web site where the login page also has fields to create a login/account. So when you click on the Login link from the Home page, the login page that opens has a Username and Password field on the left side for members who have an account there, and also fields on the right side of the page for those who don't - fields for them to create a username and password. On some sites LP insists on filling the U/N and P/W for creating an account instead of logging in. On other sites LP fills, say, the correct P/W field but then fills the U/N field for creating new accounts or vice versa. Or similarly, if there are U/N and P/W fields for logging in plus a field for subscribing to their newsletter, LP often fills the P/W field correctly but fills the newsletter field instead of the U/N field.
I'm not sure there can be a global fix for this as there are probably different causes at different sites, but it sure would be nice if they could somehow fix it.