Highlight post in sidebar on single page

The simplest thing would be to add a class to the link that contains the post ID.

<a href="https://wordpress.stackexchange.com/questions/97059/<?php the_permalink() ?>" class="post-<?php echo get_the_ID(); ?>">

You can then write a custom CSS function, put it in functions.php and hook to the wp_head. This function only serves to echo the necessary CSS to highlight the link.

function theme_prefix_highlight_current_post_in_sidebar() {
    if( is_single() ) {
        global $post;
    ?>
    <style type="text/css" media="screen">
        body.postid-<?php echo $post->ID; ?> a.post-<?php echo $post->ID; ?> {
            color: #f00;
        }
    </style>
    <?php
    }
}
add_action('wp_head', 'theme_prefix_highlight_current_post_in_sidebar');

EDIT: On a sidenote, if you might want to add conditional checks like is_single() in this function to only display this on the pages where it is needed.