Seeing "An error occurred in the upload..." message when calling WP Media interface on the front?
I believe, that's a core problem, but here is a workaround that I am using quite often in my projects.
Admins won't have this bug, but regular users - will. Because we are on a page, which $post was not created by this regular user, so he does not have the editing capabilities... and Media needs them.
// Preserve the current Post
// (just in case, you may not need it)
$oldPost = $GLOBALS['post'];
// Make it a dummy
$GLOBALS['post'] = 0;
// For example, the editor, with "Media" button:
wp_editor($content, $editor_id, $settings);
// Or "Upload Avatar" code from the WPUA plugin
do_action( 'show_user_profile', $current_user );
$GLOBALS['post'] = $oldPost;
// Be happy