While some aren't necessarily going to be a problem, errors indicating unclosed tags and stray end tags indicates that the HTML isn't well formed, which means you're likely to have knock on errors. In this case, I wouldn't be surprised if the page-specific breadcrumb issues are caused by this malformed HTML.
No. The breadcrumb code shouldn't have any problems. The issues are likely to be the custom HTML you've defined (which is part of your page node) as broken HTML there can have knock on effects elsewhere.