So, two separate issues – links not displaying and faulty markup?
For links not displaying – check if your template uses the_content() function, more functionality doesn’t display links after the_excerpt().
For markup I find that you need blank lines around more for everything to work properly.
So this can cause markup issues:
Some text here.
<!--more-->
And more here.
But this works fine:
Some text here.
<!--more-->
And more here.