Not always, POD often demands completely empty lines !

> displaying underscores for whitespaces is very confusing.

I know what you mean, but it's not an underscore it's underlined! 8)

You can either switch it off  (setq cperl-invalid-face nil)

Or you are free to configure a new face¹ other than "underlined" to be used.

I expanded this config which I found in emacswiki:cperl-mode to default to 98% grey background. It's in my .emacs just after loading cperl-mode.

 (defface cperl-my-trailing-spaces-face
      '((((class color))
         ;; define your tastes (background, foreground)
         (
          :background "grey98" 
;         :underline "grey"
          )
         ))
      "My face for trailing spaces in cperl mode"
      :group 'cperl-mode) ; Here is the most important part. It says t
+o add
                          ; this face to the customizable group cperl-
+mode
    ;; now you can "bind" this face to cperl-invalid-face
    (set-default 'cperl-invalid-face 'cperl-my-trailing-spaces-face)
[download]

M-x customize-face cperl-my-trailing-spaces-face will show you a "GUI" to change these defaults, test and save all these face settings. Or you can click thru the menus to the customization-group "cperl-mode"

HTH!

FOOTNOTES:

¹) a face is roughly the correspondant of a CSS-class in emacs speak