Displaying a full post instead of a slug per category?

In the appropriate template file, you need to replace the_excerpt() with the_content().

As this is a change specific to a known category (i.e. “podcasts”), I would recommend creating a custom template file for that category, called category-podcasts.php, and making the change in that template file.

To create this template file, look for (in order) category.php, archive.php, or index.php. Copy whichever one you find, and rename it as category-podcasts.php.

If your Theme is loop.php-based, then you will probably want to copy loop.php as loop-podcasts.php, make the change in this file, and then call it within the category-podcasts.php template file.