There’s an excellent post here which, while it might not be completely balanced (it sets out from the start that it is against external commenting systems), it offers a good view of the cons of such systems.
A quick summary of three main points (a mixture of my personal opinions and from the blog post):
- Comments are stored externally – you no longer have ‘possession’ of the comments on your blog – they are stored by somebody else, physically away from the rest of your blog
- Comments are often loaded in via AJAX after the page has loaded, or even after they are in the viewport which can make your site appear slower to your readers
- Issues with your comments ‘provider’ may disable comment functionality – if there is a problem on IDs side you will not be able to do anything about it