First, why we need review-filters? So that people like the PHB from Dilbert can't execute their evil strategies

About the mechanics of the Yelp review filter: You won't get a formal answer here, as Yelp keeps this review filter mechanism a secret. Yelp says (and I agree) that it is easier to game the system once you know the mechanics. So any answer here would be simply a guess based on a combination of common sense and an analysis of the patterns of what reviews usually get filtered.

Here is my guess at what goes into the review-filter. (Everything is centered around Yelp's tagline: "Real people, real reviews"):

  • Number of reviews: You don't even have a Yelp account. Then, suddenly, you create a Yelp account, write a 1* review for a local business and then, you never log in back. In eyes of the review-filter, you may be a scared competitor! (or if this is a 5* review, you maybe the owner's nephew!) From whatever I have observed, perhaps more than 80% of filtered reviews are from reviewers with less than 5 reviews.
  • Number of friends: Most real people like to make friends on different social media channels, Yelp included. If you don't want your Facebook friends to see what you are writing, Yelp-filter may put you in category of review-factories, who churn out one review after another for money. This may even override the number of reviews. At least twice, I have seen a filtered review by people with 50+ Yelp reviews. In both cases, the reviewer had no Yelp friends.
  • Uniqueness of content: Real people write reviews reflecting their real experiences. If your review for a Vietnamese restaurant in Atlanta matches another reviewer's review of Thai restaurant in NYC word for word (or even 70-80%, allowing for changing some proper nouns), chances are high that at least the review published later chronologically would be filtered (if not both).
  • Other trustworthiness factors: Do you have a profile pic? Do you check-in using Yelp mobile or leave tips for other Yelpers at restaurants? Is your profile complete with all the details about your hometown, Things you love, etc? Paid reviewers may not be interested in "wasting" their time in these.
  • Location tracking: You are consistently reviewing businesses all over the US, but your IP shows that you always log in from a different country. In a different case, you, as a reviewer, log in from the same IP that is used by the business owner to log in to his business-owner account, or same IP has 25+ users registered, and all of them have just 1-2 reviews. In all these cases, your review may be flagged.

Remember that none of the above factors can be taken as a standalone factor to decide whether a review should be flagged. Your review may be totally genuine, even if one or more factors above indicate otherwise. My guess is that the filter may be working using a filter-score (similar to spam score used by Anti-spam filters) assigning scores to the factors above (and many more). Once your review crosses a certain threshold, it gets filtered!

See question on Quora