Error display post thumbnails for previous and next post

That message is a general PHP error saying that you are trying to use a variable like a PHP object when it is not a PHP object. If you read the docs for get_previous_post() and get_next_post(), you can see that those functions return a post object or null/empty string if the previous/next post couldn’t be determined. So, you need to check that you have an object before trying to use it:

$prev_post = get_previous_post(true);
if( is_object( $prev_post ) ) {
    $prev_thumbnail = get_the_post_thumbnail ( $prev_post->ID, array(100, 100) );
    previous_post_link( $prev_thumbnail . '%link', '<span class="prev-link"> <span>Previous Post</span> <br/> %title </span>'  );
}

$next_post = get_next_post(true);
if( is_object( $next_post ) ) {
    $next_thumbnail = get_the_post_thumbnail ( $next_post->ID, array(100, 100) );
    next_post_link( $next_thumbnail . '%link', '<span class="next-link"><span>Next Post </span><br/> %title </span>' );
}