Apparently a big one is signing up to SEO forums with keyword-laced usernames and signature links, asking random SEO questions you already know the answer to, and overall wasting space on the site as well as peoples' time.

The lines are coming from borders on the link items in the menus (see style.css.php, line 122).
My recommendation is that you add class="first" to the first <a> tag in each menu, and class="last" to the last <a> tag in each menu. Then in your CSS, create new rules:

div.menu a.first { left-border: 0; }
div.menu a.last { right-border: 0; }

Edit: To get rid of the extra line at the bottom of the Latest News box, delete the last <div class="innerline"> </div>.
You may also want to read up on modern web standards, especially XHTML 1.0 Transitional, as that's the DOCTYPE you're using. <font> tags are deprecated (that means old and out of use), and they should not contain other <font> tags and certainly not <div> tags. Further, general practice for nav menus in XHTML is to use unordered lists, such as

<ul class="menu">
    <li><a href="...">Item1</a></li>
    <li><a href="...">Item1</a></li>
</ul>
zobadof commented: Didn't actually resolve it at all, changed nothing. +0