I am having the same issue with not being able to Delete posts from the dashboard, but I am fulling able to delete from within the backend.
When I try to delete a custom post type, even as the admin, my wordpress admin bar goes white, my header stays the same, but the rest of the site goes white and nothing happens. When I go back into the users dashboard, the post is still there.
Again, going into the backend I am able to delete without any problems.
Well I have a lot of plugins on the site, but the main ones I use for the uploading would be:
Theme My Login – for the login screen and to avoid using wp-admin to login in
Buddypress – for all the accounts that are set up
WP User Frontend Pro – to upload posts to custom post types with taxonomies
Email Login – to give the users the ability to use their email to login
Ultimate CMS – to create the custom post types and taxonomies
I did have W3 Total Cache and WP Super Cache installed at times (I was testing them both) but both have since been deleted. I have also deleted any unused plugins on my site.
I also used to have WP User Frontend and it worked without any issues, however I never used it with Custom Post Types or Taxonomies.