Ok - got the answer from WooCommerce. For anyone having the problem here, this is the answer:
Sadly WordPress doesn't update old roles with new capabilities on its own. You'll need to do this manually using http://wordpress.org/extend/plugins/capsman/
This is the full list of capabilities the shop manager should be given:
add_role('shop_manager', __('Shop Manager', 'woocommerce'), array(
'read' => true,
'read_private_pages' => true,
'read_private_posts' => true,
'edit_posts' => true,
'edit_pages' => true,
'edit_published_posts' => true,
'edit_published_pages' => true,
'edit_private_pages' => true,
'edit_private_posts' => true,
'edit_others_posts' => true,
'edit_others_pages' => true,
'publish_posts' => true,
'publish_pages' => true,
'delete_posts' => true,
'delete_pages' => true,
'delete_private_pages' => true,
'delete_private_posts' => true,
'delete_published_pages' => true,
'delete_published_posts' => true,
'delete_others_posts' => true,
'delete_others_pages' => true,
'manage_categories' => true,
'manage_links' => true,
'moderate_comments' => true,
'unfiltered_html' => true,
'upload_files' => true,
'export' => true,
'import' => true,
'manage_woocommerce' => true,
'manage_woocommerce_orders' => true,
'manage_woocommerce_coupons' => true,
'manage_woocommerce_products' => true,
'view_woocommerce_reports' => true
));
After you've given the shop_manager these capabilities (using the plugin I linked to) they will be able to view and edit products as normal.
Thanks