Similar to this post (http://wordpress.org/support/topic/plugin-w3-total-cache-error-403-forbidden), I am getting 403 Forbidden errors on cached pages when I use Disk:Enhanced Page Cache.
Disk:Basic works fine for Page Cache. Opcode APC also works fine for Page Cache, but doesn't actually cache any pages on the server (i.e. no static hml pages get created when the page is visited regardless of whether I am logged in or not when viewing the pages in a browser).
My root htaccess file has these directives in it:
# BEGIN W3TC Browser Cache
<IfModule mod_deflate.c>
<IfModule mod_headers.c>
Header append Vary User-Agent env=!dont-vary
</IfModule>
AddOutputFilterByType DEFLATE text/css text/x-component application/x-javascript application/javascript text/javascript text/x-js text/html text/richtext image/svg+xml text/plain text/xsd text/xsl text/xml image/x-icon application/json
<IfModule mod_mime.c>
# DEFLATE by extension
AddOutputFilter DEFLATE js css htm html xml
</IfModule>
</IfModule>
# END W3TC Browser Cache
# BEGIN W3TC Page Cache core
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{HTTP:Accept-Encoding} gzip
RewriteRule .* - [E=W3TC_ENC:_gzip]
RewriteCond %{REQUEST_METHOD} !=POST
RewriteCond %{QUERY_STRING} =""
RewriteCond %{REQUEST_URI} \/$
RewriteCond %{HTTP_COOKIE} !(comment_author|wp\-postpass|w3tc_logged_out|wordpress_logged_in|wptouch_switch_toggle) [NC]
RewriteCond "%{DOCUMENT_ROOT}/wp-content/cache/page_enhanced/%{HTTP_HOST}/%{REQUEST_URI}/_index.html%{ENV:W3TC_ENC}" -f
RewriteRule .* "/wp-content/cache/page_enhanced/%{HTTP_HOST}/%{REQUEST_URI}/_index.html%{ENV:W3TC_ENC}" [L]
</IfModule>
# END W3TC Page Cache core