checkboxes into a multiple selection input

You have to describe how it's breaking? Is the Ruby not running or does the client side looks broken? If so where in the Ruby code is causing the error and how does the broken client side code look? Maybe even copy and paste the resulting clientside code?

I'll try to guess what you did wrong and make a response anyway.

First, you should always indent your code properly.

Second, your </div> should be placed out side the <% end %>

<div id="taxons_offered">
    <h3>Taxonomies Offered In</h3>
    <% for store in Store.all %>
        <% if store.has_taxonomies? %>
            <div store_id='<%= store.id %>'> 
            <h4><%= store.name %></h4>
            <ul class="multi-column-checkbox">
                <% for taxonomy in store.taxonomies %>
                    <li><%= check_box_tag "idea[taxonomy_ids][]",   
     taxonomy.id, @idea.taxonomies.include?(taxonomy) %> <%= taxonomy.name %></li>
                <% end %>
            </ul>
        <% end %>
    <% end %>
</div>

Try the code above and tell me if that makes any difference.