The problem is that you have to click on a link and open a new page to listen to the voicemail. If you enable "Google Voice player in mail" in Gmail Labs, you can play voicemails in Gmail.
"Best of all, your message status will stay synced: messages played from Gmail will appear as read in your Google Voice inbox and won't be played again when you check new messages via your phone," explains the Gmail blog.
A simple Google search lets you find some public voicemails and their transcriptions, but it's worth pointing out that sharing your voicemail is optional.
While this feature is useful, it's limited to Google Voice. Gmail should provide a scripting framework like Google Apps Scripts that lets you add features and handle repetitive tasks.