Plugin for handling the URLs to make infinite scrolling work properly on pages like this http://www.pewresearch.org/category/publications/

pew-infinite-scroll.js

jQuery(document).ready(function() {
	//Set-up some constants.
	var scrollTimeout;
	var scrollUsePushStateInstead = false; //Set to true to make the history stack of the browser include every point when posts were loaded. It's kind of annoying.
	var scrollDelay = 200; //Milliseconds
	var scrollLoading = false;
	var triggerOffset = $(document).height() - $('#pagination').siblings().eq(-4).offset().top; //The point of this is to do one calculation up front instead of multiple calculations every time the infinite scroll is triggered. 
	
	// Simple feature detection for History Management (borrowed from Modernizr)
	function supportsHistory() {
		return !!(window.history && history.pushState);
	}
	
	if( supportsHistory() ) {
		$(window).on('scroll', function() {
			toInfinityAndBeyond();
		});
	}
	
	//The function that does all of the work.
	function toInfinityAndBeyond() {
		if( scrollLoading ) {
			return;
		}
		//if( scrollTrigger < $(document).scrollTop()) {
		if( $(document).height() - triggerOffset < $(document).scrollTop() + $(window).height() ) {
			var nextURL = $('#pagination').find('.next').eq(0).attr('href');
			if( !nextURL ) {
				return;
			}
			
			$.ajax({
				type: 'GET',
				url: nextURL,
				beforeSend: function() {
					// block potentially concurrent requests
					scrollLoading = true;
				},
				success: function(data) {
					$('#pagination').before( $(data).find('#content').html() ).remove();
					
					var newPageNum = nextURL.match(/\/page\/(\d+)\//)[1];
					
					regexp = /\/(pages?)\/([0-9]+)-?([0-9])*\/?$/;
					var newPath = window.location.href;
					if( regexp.test(newPath) ) {
						parts = regexp.exec(newPath);
						//Assign different parts to more understandable labels. Assume the following example: http://example.com/thing/pages/2-4/
						matchingPattern = parts[0]; // -> /pages/2-4/
						pageLabel = parts[1].toLowerCase(); // -> pages
						pageStart = parts[2]; // -> 2
						pageEnd = parts[3]; // -> 4
						
						if( pageEnd > 0 && pageStart == 1 ) {
							pageStart = pageEnd;
							pageEnd = false;
						}
						
						var blackMagic = new RegExp(matchingPattern, 'ig');
						
						//We're dealing with /pages/x-x/
						replacement = '/pages/' + pageStart + '-' + newPageNum + '/';
						if( !pageEnd ) {
							//We're dealing /page/x/ or /pages/x/
							replacement = '/pages/' + newPageNum + '/';
							if( pageLabel == 'page' ) {
								replacement = '/pages/' + pageStart + '-' + newPageNum + '/';
							}
							
						}
						
						newPath = newPath.replace( blackMagic, replacement);
					} else {
						//There is no /page/ or /pages/ in the URL. We'll assume we can just append a new /pages/ path to the current URL.
						newPath += 'pages/' + newPageNum + '/';
					}		
					
					newPath = '/' + newPath.split('/').slice(3).join('/');
					if( scrollUsePushStateInstead ) {
						window.history.pushState(null, null, path);
					} else {
						window.history.replaceState(null, null, newPath);
					}
					
					// unblock more requests (reset loading status)
					scrollLoading = false;
					
				},
				dataType: "html"
			});	
		}
	}
});

pew-infinite-scroll.php

<?php
/*
Plugin Name: Pew Infinite Scroll
Description: "To infinity... and beyond!" 
Author: Russell Heimlich
Author URI: http://www.russellheimlich.com/
Version: 0.1
*/

//Lets make rewrites work properly
//$pageregex = $this->pagination_base . '/?([0-9]{1,})/?$';
function pew_infinite_scroll_rewrite_rules() {
	/*
	global $wp_rewrite;
	$rewrite_tags = array(
		array( '%pages%', '/?([0-9]{1,}\-[0-9]{1,})/?$', 'pages='),
	);
	foreach( $rewrite_tags as $tag ):
		$wp_rewrite->add_rewrite_tag( $tag[0], $tag[1], $tag[2] );
	endforeach;
	*/
	
	add_rewrite_endpoint( 'pages', EP_ALL );
}
add_action('init', 'pew_infinite_scroll_rewrite_rules');

function pew_infinite_scroll_pre_get_posts( $query ) {
    if ( is_admin() || !$query->is_main_query() )
        return;
		
	
	if ( $query->is_archive() && ( $pages = pew_infinite_scroll_get_pages() ) ) {
		$start = $pages->start;
		
		if( $start == -1 ) {
			$query->set( 'nopaging', true );
		} else {
			$query->set( 'paged', $start );
		}
		
		return;
	}
}
add_action( 'pre_get_posts', 'pew_infinite_scroll_pre_get_posts' );

function pew_infinite_scroll_post_limits( $limit ) {
	global $wp_query;
	if ( is_admin() || !$wp_query->is_main_query() ) {
		return $limit;	
	}
	
	if( $pages = pew_infinite_scroll_get_pages() ) {
		if( $pages->start == -1 ) {
			return $limit;
		}
		
		$new_limit = $pages->diff * $pages->posts_per_page + $pages->posts_per_page;
		$limit = str_replace(', ' . $pages->posts_per_page, ', ' . $new_limit, $limit);	
	}
	return $limit;
}
add_filter( 'post_limits', 'pew_infinite_scroll_post_limits' );

function pew_infinite_scroll_wp() {
	global $wp_query, $paged;
	$pages = pew_infinite_scroll_get_pages();
	if( !$pages || !$pages->end ) {
		return;
	}
	
	$wp_query->set('paged', $pages->end);
	$paged = get_query_var( 'paged' );
}
add_action( 'wp', 'pew_infinite_scroll_wp' );

function pew_infinite_scroll_redirect_canonical( $redirect_url, $requested_url ) {
	//Kill the canonical 'paged' redirect if the pages query var is set. In other words we don't want /category/publications/?pages=1-10 to redirect to /category/publications/page/10/?pages=1-10 which is what would happen by default.
	if( get_query_var('pages') ) {
		$redirect_url = trailingslashit($requested_url);	
	}
	return $redirect_url;
}
add_filter( 'redirect_canonical', 'pew_infinite_scroll_redirect_canonical', 10, 2 );

function pew_infinite_scroll_get_pagenum_link($result) {
	if( $pages = pew_infinite_scroll_get_pages() ) {
		$result = preg_replace('/pages\/([\d\-]+|all)\//i', '', $result); //Strip out anything that matches pages/{any digit or hypen or the word all}/
		
	}
	return $result;
}
add_filter('get_pagenum_link', 'pew_infinite_scroll_get_pagenum_link');

function pew_infinite_scroll_enqueue_script() {
	if( is_archive() ) {
		wp_enqueue_script( 'pew-infinite-scroll' );
	}
}
add_action( 'wp_enqueue_scripts', 'pew_infinite_scroll_enqueue_script' );


/***
* Helper Functions
***/

function pew_infinite_scroll_get_pages() {
	$pages_var = get_query_var('pages');
	if( !$pages_var ) {
		return false;
	}
	$start = 1;
	$end = false;
	$pages = explode( '-', $pages_var );
	
	if( count($pages) < 2 && isset($pages[0]) && !empty( $pages[0] ) ) {
		if( strtolower($pages[0]) == 'all' ) {
			$start = -1;
			$end = false;
		} else {
			$end = intval($pages[0]);
		}
	} else {
		$pages = array_map('intval', $pages);
		if( isset($pages[0]) && !empty( $pages[0] ) ) {
			$start = $pages[0];
		}
		
		if( isset( $pages[1] ) && !empty( $pages[1] ) ) {
			$end = $pages[1];
		}
	}
	
	return (object) array(
		'start' => $start,
		'end' => $end,
		'diff' => abs( $end - $start ),
		'posts_per_page' => intval(get_option('posts_per_page'))
	);
}

Recommended reading:

1. http://tumbledry.org/2011/05/12/screw_hashbangs_building
2. http://googlewebmastercentral.blogspot.com/2014/02/infinite-scroll-search-friendly.html