Toolset: WordPress 3.9, Social 2.11, and Twitter Embed 1.1.1 the only other plugin that touches Twitter.
When I set "Pull in social comments from Facebook and Twitter" to Yes, I will get a spate of imported comments that have nothing to do with my timeline or the URL posted. I will get comments on each of the posts on the front page. At present, I have 149 comments sitting in the moderation queue, all repeats on different posts.
I have disconnected and reconnected Twitter within Social, but the problem persisted. I'm going to disconnect for now but will be happy to help test the problem.