Calling the_excerpt from inside a plugin template file

You are doing few things wrong:

  1. the_excerpt does not uses post id.
  2. When you modify global $post you should always set it back to its original value.
  3. you were assigning get_post’s return value to $p which was not used in your code.

I have made few fixes in your code. The below code is just the copy paste of your code with my fixes so try the code below and let me know if you still have issues. Sorry I had to change bit of your code formatting.

<?php
    if (!empty($user)):
        if (!wpfp_is_user_favlist_public($user)):
            echo "$user's Favorite Posts.";
        else:
            echo "$user's list is not public.";
        endif;
    endif;

    if ($wpfp_before):
        echo "<p>".$wpfp_before."</p>";
    endif;

    if ($favorite_post_ids):
        foreach ($favorite_post_ids as $post_id) {
            $p = get_post($post_id);
?>
      <div class="homepage_props">

                       <div class="homepage_props_inner">
                            <div class="homepage_propsbanner">
                                <div class="homepage_new">
                                <?php if (strtotime($p->post_date) > strtotime('-7 days')) { ?>
                                    <img src="https://wordpress.stackexchange.com/questions/20161/<?php echo get_template_directory_uri(); ?>/images/new.png" alt="latest property listings" />
                                <?php } ?>
                                </div>
                                <h2><span style="float:left; font-weight:bold;">
                                <?php 
                                    if ( 'sales' == $p->post_type ) { 
                                        echo 'Property For Sale'; 
                                    } elseif ( 'rentals' == $p->post_type ) {
                                        echo 'Property For Rent'; 
                                    } elseif ( 'business' == $p->post_type ) { 
                                        echo 'Business For Sale'; 
                                    } elseif ( 'bandb' == $p->post_type ) {
                                        echo 'Bed And Breakfast'; 
                                    } 
                                ?>
                                </span>
                                <span style="float:right; font-weight:normal;">
                                    <a href="<?php echo get_permalink($post_id); ?>" title="<?php printf( esc_attr__( 'Permalink to %s', 'themename' ), get_the_title( $post_id ) ); ?>" rel="bookmark"><?php echo get_the_title ( $post_id ); ?></a>
                                </span>
                                </h2>
                            </div>

                            <div class="clear"></div>
                                  <div class="homepage_props_image">
<?php  

        echo "<a href="".get_permalink($post_id)."">";
        echo get_the_post_thumbnail ( $post_id, 'medium' );
        echo "</a>";

?>
                                   </div><!-- / homepage_props_image -->

                                           <div class="homepage_props_info hyphenate">

                                           <?php echo $p->post_excerpt; ?>

                                           </div><!-- / homepage_props_info -->

                                                     <div class="clear"></div>

                                            <div class="homepage_props_tax">

                                    <?php 
                                        if ( in_array( $p->post_type, array( 'sales', 'rentals', 'business' ) ) ) {
                                            echo '<h3><span style="float:right; font-weight:normal;">' .get_the_term_list( $post_id, 'property_type', 'Property Type: ', ' ', '' ),'&nbsp;&nbsp;&nbsp;' .get_the_term_list( $post_id, 'location', 'Location: ', ' ', '' ),'&nbsp;&nbsp;&nbsp;'.get_the_term_list( $post_id, 'region', 'Region: ', ' ', '' );
                                            echo '</span></h3>';
                                        } 
                                    ?>
                                            </div><!-- / homepage_props_tax -->



                   </div><!-- / homepage_props_inner -->

                 </div><!-- / homepage_props -->

<?php
        }
    else:
        echo $wpfp_options['favorites_empty'];
    endif;
?>