I used to be a newspaper art critic, so I have plenty of practice at screening out the influence of other comments and concentrating on my own reactions. Of course, critiquing a single photo is very different from writing about an entire exhibit, in which case you're trying to state some kind of thesis involving the artist's or curator's dominant themes and trends, and then back that up with reference to individual works -- all the while trying to avoid boring the reader (who probably hasn't seen the exhibit) into a stupor!
When picking work to critique in the RFF gallery, I start by choosing pictures that strike me in some positive way. (We're all friends here, so there's no point in picking out an especially bad photo to give it a hatchet-job. That's sometimes necessary in professional art criticism -- especially when a highly-touted exhibit or artist fails to live up to the hype, and has to be ventilated for the sake of viewers who might otherwise be cowed into doubting their own judgment.)
Having picked a photo on which to comment, I try to analyze and explain briefly WHY I like it: Is it the appeal of the subject, the atmosphere, the technical brilliance? Really successful photos seldom succeed only on one level, so I also try to devote a few words to how its secondary characteristics reinforce its primary appeal: for example, a photo of an appealing subject that also happens to have an especially pleasing tonal range.
Then, since people presumably post their photos for critiques hoping to learn something that will help their future photography, I try to identify one or two areas in which the photo falls somewhat short, and (if possible) offer a suggestion or two that might be useful next time.
I don't overemphasize this, though -- I feel that actually the most useful part of the critique is identifying the successful elements of the photo. A few years ago I read an interesting article in a management newsletter, by a psychologist who had been doing studies challenging many old assumptions about learning and training. One he especially disputed was the old saw that you learn from your mistakes. In fact, he said, his research shows that you learn most from your successes -- he suggested concentrating on them, trying to learn WHY they succeeded, and then apply the learning to other situations. I think that's a good model for a successful short critique.