You want your site to be a social object. That means it makes sense to connect to whatever platform where people are talking about you and the content, value you provide. However, here's the rub. You are also a curator, and right now one of the most valuable things you can do for your customers, consumers, employees or business partners is to filter signal from noise.
So while you may benefit from publishing every retweet of your content because it links to someone, you have to do this by design realizing that it may not benefit the person who is looking for value in your content. So who is doing it right?
Well, I've always been a fan of how Chris Brogan curates things over at his place. Not only is it easy for someone to comment, but it's personal using a service which provides the photo of the commenter giving them more incentive to participate. But specifically to the issue of integration with something like Twitter, Chris calls this out as "reactions". And yes, that makes all the difference. Why? Because it's more accurate and has been thought through purposefully.
Technology allows us to do all sorts of great things, but without purpose or intentâ€"we can unintentionally provide a less than desirable experience. If I had more technical mastery and time to dedicate to this blog, I'd go the route that Chris has been paving when it comes to curating comments on your social properties. A simply label followed by hierarchy of what you display and how you display it can make all the difference. It might even be worth calling out the things that are not comments but reactions as a feature on the same level as comments.
But this might require the blogging platforms to evolve. Until then, remember that you have to decide what your goals are for yourself or your organization before displaying how you integrate. Be mindful of your signal to noise ratio and what you vs. your participants get from it. And as Brogan's example illustrates, put some thought into how you display it.