Really sorry about that.
We put a lot of work into validating our rewriters against a large corpus of websites and we disable filters that cause problems as soon as we can, but sometimes things slip through.
Please disable compression in any WordPress plugin you are using, so that mod_pagespeed will process uncompressed HTML. mod_pagespeed ensures that its output will be compressed by enabling mod_deflate.
If it's still breaking your site, please try appending ?ModPagespeed=off to the URL.
This deactivates PageSpeed.
If the site is still broken, it is not a rewrite or HTML parsing problem.
If that fixed the site, try appending ?ModPagespeed=on&ModPagespeedFilters= to the URL.
This turns on PageSpeed, but no filters.
If the site is broken now, it is an HTML parsing problem.
If the site still worked, try appending ?ModPagespeed=on&ModPagespeedFilters=foo for various filters "foo".
For example try:
https//domain.com/?ModPagespeed=on&ModPagespeedFilters=extend_cache https//domain.com/?ModPagespeed=on&ModPagespeedFilters=combine_css https//domain.com/?ModPagespeed=on&ModPagespeedFilters=inline_css https//domain.com/?ModPagespeed=on&ModPagespeedFilters=inline_javascript https//domain.com/?ModPagespeed=on&ModPagespeedFilters=insert_image_dimensions https//domain.com/?ModPagespeed=on&ModPagespeedFilters=rewrite_images https//domain.com/?ModPagespeed=on&ModPagespeedFilters=rewrite_css https//domain.com/?ModPagespeed=on&ModPagespeedFilters=rewrite_javascript
You may have to reload them a few times over several seconds to make sure they have had time to load sub-resources into the cache and rewrite them.
If one of these breaks your site, you now know which filter is at fault.