Yes - You can bulk approve posts or comments using the bulk editing feature located under the list view. To change your homepage to list view, click the small view icon located above the search box.
First, filter your homepage to view only unapproved posts or comments. This is done by clicking the small orange circle indicating the number of unapproved posts or comments in your class. Next, check the small box next to the posts or comments to be approved. Click the small blue "Edit" button at the top of the page and select the desired published status of the selected posts or comments.