Redirection not working in this front end post submission form?

Your code is not in the right order and you need to exit the script after using wp_redirect try this:

<?php 
/* 
Template Name: Rate Wine Form 
*/
?> 
<?php 
if( 'POST' == $_SERVER['REQUEST_METHOD'] && !empty( $_POST['action'] ) &&  $_POST['action'] == "new_post") { 

    // Do some minor form validation to make sure there is content 
    if ($_POST['title'] != '') { 
        $title =  $_POST['title']; 
    } else { 
        echo 'Please enter the wine name'; 
        return false;
    } 
    if (isset ($_POST['description'])) { 
        $description = $_POST['description']; 
    } else { 
        echo 'Please enter some notes'; 
    } 

    $tags = $_POST['post_tags']; 
    $winerating = $_POST['winerating']; 

    // ADD THE FORM INPUT TO $new_post ARRAY 
    $new_post = array( 
    'post_title'    =>   $title, 
    'post_content'  =>   $description, 
    'post_category' =>   array($_POST['cat']),  // Usable for custom taxonomies too 
    'tags_input'    =>   array($tags), 
    'post_status'   =>   'publish',           // Choose: publish, preview, future, draft, etc. 
    'post_type' =>   'post',  //'post',page' or use a custom post type if you want to 
    'winerating'    =>   $winerating
    ); 

    //SAVE THE POST 
    $pid = wp_insert_post($new_post); 

             //KEEPS OUR COMMA SEPARATED TAGS AS INDIVIDUAL 
    wp_set_post_tags($pid, $_POST['post_tags']); 



    //ADD OUR CUSTOM FIELDS 
    add_post_meta($pid, 'rating', $winerating, true);  

    //INSERT OUR MEDIA ATTACHMENTS 
    if ($_FILES) { 
        foreach ($_FILES as $file => $array) { 
        $newupload = insert_attachment($file,$pid); 
        // $newupload returns the attachment id of the file that 
        // was just uploaded. Do whatever you want with that now. 
        } 

    } // END THE IF STATEMENT FOR FILES 


    //redirect to newly created post
    wp_redirect( get_permalink($pid) ); 
    exit();
} // END THE IF STATEMENT THAT STARTED THE WHOLE FORM 

?> 


        <div id="container"> 
            <div id="content" role="main"> 

        <!-- WINE RATING FORM --> 

        <div class="wpcf7"> 
        <form id="new_post" name="new_post" method="post" action="" class="wpcf7-form" enctype="multipart/form-data"> 
            <!-- post name --> 
            <fieldset name="name"> 
                <label for="title">Wine Name:</label> 
                <input type="text" id="title" value="" tabindex="5" name="title" /> 
            </fieldset> 

            <!-- post Category --> 
            <fieldset class="category"> 
                <label for="cat">Type:</label> 
                <?php wp_dropdown_categories( 'tab_index=10&taxonomy=category&hide_empty=0' ); ?> 
            </fieldset> 

            <!-- post Content --> 
            <fieldset class="content"> 
                <label for="description">Description and Notes:</label> 
                <textarea id="description" tabindex="15" name="description" cols="80" rows="10"></textarea> 
            </fieldset> 

            <!-- wine Rating --> 
            <fieldset class="winerating"> 
                <label for="winerating">Your Rating</label> 
                <input type="text" value="" id="winerating" tabindex="20" name="winerating" /> 
            </fieldset> 

            <!-- images --> 
            <fieldset class="images"> 
                <label for="bottle_front">Front of the Bottle</label> 
                <input type="file" name="bottle_front" id="bottle_front" tabindex="25" /> 
            </fieldset> 

            <fieldset class="images"> 
                <label for="bottle_rear">Back of the Bottle</label> 
                <input type="file" name="bottle_rear" id="bottle_rear" tabindex="30" /> 
            </fieldset> 

            <!-- post tags --> 
            <fieldset class="tags"> 
                <label for="post_tags">Additional Keywords (comma separated):</label> 
                <input type="text" value="" tabindex="35" name="post_tags" id="post_tags" /> 
            </fieldset> 

            <fieldset class="submit"> 
                <input type="submit" value="Post Review" tabindex="40" id="submit" name="submit" /> 
            </fieldset> 

            <input type="hidden" name="action" value="new_post" /> 
            <?php wp_nonce_field( 'new-post' ); ?> 
        </form> 
        </div> <!-- END WPCF7 --> 

            </div><!-- #content --> 
        </div><!-- #container -->