Scott Reilly

How far into the instructions have you gotten, beyond installing the plugin? Do you have the images named a ‘nice-name’ version of the category name (i.e. the category name, but lower-cased, and with all non-alphanumeric characters removed and spaces replaced with underscores… so the category “Fun and Games!” would need a file “fun_and_games.png” (or of some other image extension)).
Then, in your index.php, replace:
<?php the_category() ?>
with something like:
<?php the_category_image(' '); ?>
You’ll have to possibly send different arguments depending on if your situation, in terms of image extension and image directory, differs from the default.

How many commenters do you have to your site? By default, it identifies commenters by the e-mail they provide, so if no e-mail is used, then the commenter gets omitted from the listing. (commenters can also be identified by name instead). It looks like it may be treating “tim ” (with space) differently than “tim”, but my guess would be that tim posted comments using different e-mail addresses?
You don’t need anything from the ‘outputs’ section. You just need to add something like:

and/or

to your index.php

For #1, to show category description at top of category page (I’m assuming that the text you want at the top of the category pages is the description you defined for the category in the Admin section)
In index.php, look for this:
<?php if ($posts) : foreach ($posts as $post) : start_wp(); ?>
Change it to this:
<?php if ($posts) : ?>
<?php if ($cat) : ?>
<p class="cat-description"><?php echo category_description(); ?>
<?php endif; ?>
<?php foreach ($posts as $post) : start_wp(); ?>
You’ll see the category description, and will be able to style it with CSS by addressing the ‘cat-description’ class.

joand: You found the right bit of code. You have to change the line:
$output .= ' \">$more_link_text";
to be:
$output .= ' \">$more_link_text";
(Basically getting rid of #more-$id)

The function comments_popup_script() is located in wp-includes/template-functions-comment.php. It contains the javascript in the function itself and does not use an external .js file.

My guess is that you have this option set: “WordPress should correct invalidly nested XHTML automatically” (Admin page -> Options menu -> Writing submenu). In certain circumstances it may do what you describe. I’ve documented some of the issues with that setting.
To test for certain: disable the setting, go back to the post you were having problems with, fix it, and save it. If it came out alright, then that setting was the culprit. Please do give us an idea of what precisely went wrong when the setting was on, or point us to the post and tell us what tag got chopped off.

Do you close out the php tag at the end of your snippet, like so:
<?php next_post('%','Next Entry<img src="http://www.bbiverson.com/images/buttons/next.jpg" alt="Read Next Entry" align="middle" />','no','no',1,'');
} ?>

Or there’s this, Top/Recent Commenters plugin.
/plug