How to fix E_DEPRECATED with SImple Footnotes WP plugin and PHP 7

simple-footnotes.php

<?php
/*
 * Plugin Name: Simple Footnotes
 * Plugin URI: http://wordpress.org/extend/plugins/simple-footnotes/
 * Plugin Description: Create simple, elegant footnotes on your site. Use the <code>[ref]</code> shortcode ([ref]My note.[/ref]) and the plugin takes care of the rest. There's also a <a href="options-reading.php">setting</a> that enables you to move the footnotes below your page links, for those who paginate posts.
 * Version: 0.3
 * Author: Andrew Nacin
 * Author URI: http://andrewnacin.com/
 */
class nacin_footnotes {
        var $footnotes = array();
        var $option_name = 'simple_footnotes';
        var $db_version = 1;
        var $placement = 'content';
        function __construct() {
                add_shortcode( 'ref', array( &$this, 'shortcode' ) );
                $this->options = get_option( 'simple_footnotes' );
                if ( ! empty( $this->options ) )
                        $this->placement = $this->options['placement'];
                if ( 'page_links' == $this->placement )
                        add_filter( 'wp_link_pages_args', array( &$this, 'wp_link_pages_args' ) );
                add_filter( 'the_content', array( &$this, 'the_content' ), 12 );
                if ( ! is_admin() )
                        return;
                add_action( 'admin_init', array( &$this, 'admin_init' ) );
        }
        function nacin_footnotes() {
		self::__construct();
        }
        function admin_init() {
                if ( false === $this->options || ! isset( $this->options['db_version'] ) || $this->options['db_version'] < $this->db_version ) {
                        if ( ! is_array( $this->options ) )
                                $this->options = array();
                        $current_db_version = isset( $this->options['db_version'] ) ? $this->options['db_version'] : 0;
                        $this->upgrade( $current_db_version );
                        $this->options['db_version'] = $this->db_version;
                        update_option( $this->option_name, $this->options );
                }
                add_settings_field( 'simple_footnotes_placement', 'Footnotes placement', array( &$this, 'settings_field_cb' ), 'reading' );
                register_setting( 'reading', 'simple_footnotes', array( &$this, 'register_setting_cb' ) );
        }
        function register_setting_cb( $input ) {
                $output = array( 'db_version' => $this->db_version, 'placement' => 'content' );
                if ( ! empty( $input['placement'] ) && 'page_links' == $input['placement'] )
                        $output['placement'] = 'page_links';
                return $output;
        }
        function settings_field_cb() {
                $fields = array(
                        'content' => 'Below content',
                        'page_links' => 'Below page links',
                );
                foreach ( $fields as $field => $label ) {
                        echo '<label><input type="radio" name="simple_footnotes[placement]" value="' . $field . '"' . checked( $this->placement, $field, false ) . '> ' . $label . '</label><br/>';
                }
        }
        function upgrade( $current_db_version ) {
                if ( $current_db_version < 1 )
                        $this->options['placement'] = 'content';
        }
        function shortcode( $atts, $content = null ) {
                global $id;
                if ( null === $content )
                        return;
                if ( ! isset( $this->footnotes[$id] ) )
                        $this->footnotes[$id] = array( 0 => false );
                $this->footnotes[$id][] = $content;
                $note = count( $this->footnotes[$id] ) - 1;
                return ' <a class="simple-footnote" title="' . esc_attr( wp_strip_all_tags( $content ) ) . '" id="return-note-' . $id . '-' . $note . '" href="#note-' . $id . '-' . $note . '"><sup>' . $note . '</sup></a>';
        }
        function the_content( $content ) {
                if ( 'content' == $this->placement || ! $GLOBALS['multipage'] )
                        return $this->footnotes( $content );
                return $content;
        }
        function wp_link_pages_args( $args ) {
                // if wp_link_pages appears both before and after the content,
                // $this->footnotes[$id] will be empty the first time through,
                // so it works, simple as that.
                $args['after'] = $this->footnotes( $args['after'] );
                return $args;
        }
        function footnotes( $content ) {
                global $id;
                if ( empty( $this->footnotes[$id] ) )
                        return $content;
                $content .= '<div class="simple-footnotes"><p class="notes">Notes:</p><ol>';
                foreach ( array_filter( $this->footnotes[$id] ) as $num => $note )
                        $content .= '<li id="note-' . $id . '-' . $num . '">' . do_shortcode( $note ) . ' <a href="#return-note-' . $id . '-' . $num . '">&#8617;</a></li>';
                $content .= '</ol></div>';
                return $content;
        }
}
new nacin_footnotes();

Glad i came across this - i have a client using this plugin across a few thousand articles and the need to make this PHP 8+ compatible is growing. Can you confirm whether this update fixes that compatibility (Nacin's original code wasn't.)

I can't confirm. Currently I don't have any PHP 8 installation available. But it shouldn't be difficult for you if you have one. :-)