Should I write a peer-review in third person?

I recommend the first person. Like most good linguistic constructions, the reader passes over it without explicitly noticing it, whereas your first construction with "this reviewer" holds up the entire mental process for a split second.

The idea of using the third person to "soften" the criticism: well, Paul Garrett knows how much I esteem him, and we usually see eye-to-eye on things. But this time I simply disagree. The reviewer is empowered -- nay, enjoined -- to supply an opinion on the work. If you want to shade your opinion, explain very carefully and explicitly why you are doing that. Switching to the third person should not convey that you are less sure of yourself, and it does not convey that to my ear.

[Imagine my answer began with "This academic". Wouldn't that have been more distracting?]

I have a third take on the issue: this is not about the reviewer nor the author, is about the work and as such, I think that it should be the subject of the sentence:

The paper could benefit from a redefinition of pink elephants, possibly defining elephants in general at first and then by adding the color pink

In my opinion this has the benefit of making the review less personal and make it come through as more objective.

If you're writing a review that will be read only by the editor, you can use "I", but if you want to simplify the editor's life by giving them something to cut-and-paste, or forward, to the author:

In English, in mathematics at least, the contemporary style for publicly-consumed reviews seems to be to refer to oneself, the reviewer, as "this reviewer". Thus, "in the opinion of this reviewer...", "this reviewer cannot understand why the author is so dense..." :)

There are some observable exceptions, where a reviewer is enough of a big-shot to not merely "suggest" that the author has erred, but to be snarky about it, and in either first person, or an exaggerated third-person. My own opinion is that it is not nice to do this. That is, a forthright voice is best, and choice of voice not depending on status is tasteful.