Go to the panel's settings page: content. Edit the node that you have added and deselect "show links" (I am going from memory, I believe it is something like that).

The solution of yours worked well by hiding the "add a comment" link from inside the profile we created but the other links like tags are there yet. And also there is a "add a comment" link for the button we created(contemplate you remember) in "My account" page.

Tags are not considered as links. Here is a possible solution: http://drupal.org/node/274762

The same with the comment links on the teaser: http://drupal.org/node/65798

This thread is from a couple months back already, but I had the same goal, so I thought I'd post what I did. I found another good thread on Drupal.org that had a fairly flexible solution:
http://drupal.org/node/133236#comment-254797

Here's how I implemented it. I copied the node.tpl.php of my site's theme and created a node-profile.tpl.php file (so I won't mess with the teasers elsewhere on my site, just the profile page's).

In my custom template, I found the following line:

<?php if ($terms) { ?>
<?php print $terms?>
<?php }; ?>

Basically that just checks if there are terms, and if so, prints them. I changed the first line of this part to:

<?php if ($terms && !$teaser) { ?>

So if there are terms, AND the node being shown is NOT a teaser, it will print the terms. If it IS a teaser (like on our account page), then it won't print anything.

Same for the links section (which include the Add Comment link):

<?php if ($links): ?>
<?php print $links; ?>
<?php endif; ?>

I changed the first line to:

<?php if ($links && !$teaser): ?>

Now all I have in my teaser is my nice 'View Profile' button. Much better. :-)

(Oh, and don't forget to clear the theme registry to make Drupal see the new template!)