The most prominent social criticism in Chaucer's The Canterbury Tales is targeted at the church and its leaders.
In "The Prologue," for instance, the friar arranges marriages for women that he has impregnated. The naive narrator presents this as if it is a good thing--the friar takes care of his people kind of thing. But of course, it's not a good thing. The reader understands this.
Religious figures are, for the most part, presented as corrupt, greedy, arrogant, prideful. They are confidence, or con men.
"The Pardoner's Tale," for another example, reveals how the pardoner blatantly uses a story about greed to fulfill his own greed. The pardoner is very up front about the fact that he is just out to separate his listeners from their money.
When analyzing in search of social criticism, remember that Chaucer uses irony here. He uses the merry, naive narrator to present characters in what seems to be a positive light. The reader should understand, though, that some of the characters are not positive at all. Just because the unreliable narrator is gullible and accepts people as they are, doesn't mean the reader has to.