Dynamically output a class to an anchor tag depending on what tag is chosen

Sounds like you’d want to use this: http://codex.wordpress.org/Function_Reference/wp_get_object_terms

If you’re using a custom taxonomy, add that where it says “post_tag”.

unset($tags);
foreach(wp_get_object_terms($post->ID, 'post_tag') as $tag) :
    $tags .= ' ' . $tag->name;
endforeach;

And then add it to your anchor tag:

<a href="https://wordpress.stackexchange.com/questions/36707/<?php the_permalink(); ?>" title="View Item" class="product_view_sm<?php echo $tags; ?>">..View Item..</a>