An email account notifies you more frequently about the new comments on your website than admin area dashboard. Now-a-days, it is a lot more easier to access and reply emails directly from a smartphone; so why not use it for approving WordPress comments too?
With Gmail Comment Approval plugin you can approve comments right from your inbox, without logging in to your website’s dashboard.
The plugin works over Gmail action API and end results are just awesome.
Start by installing and activating Gmail Comment Approval plugin.
Upon activation, make sure the comment moderation option is turned on (you can easily turn on comment moderation from Settings -> Discussions page).
Now the plugin will send you new comment notifications with comment approval option which allows you to approve comments without logging back in to your WordPress site.
Troubleshooting: For this feature to work, your WordPress notification e-mails should be DKIM signed and your website must be registered with a Gmail account.