I am inclined to say that there's an increased tendency to regard dialogue as impersonal, as each truly anonymous post feels more like a one-shot contribution with no expectation of consistency or interaction, and a reduced tendency to identify directly with what you write. e.g., I may be more likely to post what I'm thinking in the moment without worrying about having to defend the position, or caring if I change my mind later. However, I strongly suspect there are confounding factors and I don't make a frequent habit of posting anonymously (Robin would probably suggest that I am too driven by status-seeking) so I can't speak terribly authoritatively on whether these impressions are accurate or if I'm repeating what I think "ought" to be the case.

For instance, one possible distracting issue is that group consensus seems to me more persuasive with increasingly anonymous discussions, and the resulting undercurrent of mob mentality presents an entirely different failure of rationality.

I've used throwaway handles to argue for views that I'm not convinced of, both to shake myself out of consistency pressures/confirmation bias and to elicit good criticism. I find that the latter is particularly helpful.