Single blind reviews can involve the author identity blind but reviewer identity disclosed, or reviewer identity blind but author identity disclosed. I assume you're asking about the latter because that is probably much more common that the former. I suppose there is some risk that the reviewers might be biased in some way or another by knowledge of the author's identity; perhaps positively toward, for example, well-regarded influential figures or, alternatively, negatively toward folks with the wrong "clan" affiliation for example. Those biases, either way, may be allowed to run somewhat unconstrained in some instances given the anonymity of the reviewers resulting from the blinding. I think, however, that most reviewers try to be fair and constructive in providing feedback in the process. For reviewers of that inclination, the single blinding should have little effect on the feedback provided. The relatively few reviewers who have less enchanting inclinations may be differently affected.

Even so, it isn't as if reviewer feedback occurs in a complete vacuum. Good editors pay attention to the feedback provided by reviewers. Most will act when they encounter reviewer feedback that deviates from being fair and constructive if only to protect the reputations of their journals. If journals are to be regarded as credible, they need to have review processes that are regarded as being fair, unbiased, and constructive. Most typically, the easiest way to deal with (positively or negatively) biased or unfair reviewers is not to invite them to review for the journal again. Other times editors can raise their concerns with reviewers more directly. A lot of variation exists on how editors deal with matters such as these. Regardless of the approach, good editors will exert influence to protect their journals. In fact, my assessment of the matter is that if the editor is a straight shooter, it matters little if the review is single or double blinded. If the editor isn't interested in the journal's reputation, however, single blind processes may offer a bit more potential downside relative to the influence of biases.

I agree with most of Robert's answer. A good editor can reduce most of these types of problems. This issue is that it does rely on a good editor. As an author who has experienced problems with a bad reviewer (i.e., would not specify the problems they thought were in the manuscript, so they could not be fixed), relying on a character of the editor often helps. However, in the cases in which it does not, the author's should be able to request a review of the process by the journal's board so that reviewers or editors that are acting unethically can be replaced without starting the process all over again. This was the case for me, but I had to fight for 8 months to have that happen. So, whether double blind or single blind, there needs to be an Ad Hoc process to mediate those cases in which an editor does not act in good faith.