Dill's mockingbird status is revealed during the trial. Specifically, he shows this side after a particularly cruel cross-examination by Mr. Gilmer. Dill and Scout go outside of the courthouse, where they encounter Mr. Dolphus Raymond. Dill explains why he is so upset about Mr. Gilmer's treatment of the witness. He compares Mr. Gilmer to Atticus Finch, and makes the point that Atticus doesn't treat witnesses like that. Mr. Raymond calms the children, and makes the statement that someday Dill will not cry about these things. It is in that moment that we see a loss of innocence by Dill. Dill sees that people are not always understanding and do not treat everyone fairly. When teaching this book, I discuss the opinion that I have that children are "color-blind" and blind to other things up to a certain age. Young children (perhaps up to around 5 or 6 years old) do not notice differences among other children. They do not notice racial differences, physical differences, and other differences that are more readily apparent to adults. All that a young child sees in another child is a fellow friend with whom he can play. In the courthouse, Dill loses his ability to be "color-blind" and therefore loses his innocence, and becomes a symbolic mockingbird.
Taken more literally, Dill is like a mockingbird in that he flits in and out of Scout and Jem's lives since he visits them only during the summertime (while he is staying with his Aunt Rachal). His cheery disposition and constant twittering (always telling stories and "stretching the truth") brighten up their lives considerably. The only exception is the one time he ran away from home and hid at the Finches (Incidentally, also the name of a species of birds) until found out.
In the symbolic context of the novel, though, I don't see Dill as being a proper example of a mockingbird since he is not really a victim in any way. He doesn't suffer from the brunt of prejudice as Tom Robinson and Boo Radley do - they are the true "mockingbirds" of this story.
As for Dill's loss of innocence, that is another question altogether.
When Dill, an orphan who visits Maycomb every summer, first introduces the idea of seeing Boo with secret missions to Jem and Scout, they make a unique friendship with Boo. This friendship with Boo brings them gifts and eventually saves their lives. Without Dill's curiosity, which partakes in the friendship with Boo, Bob Ewell probably would have killed both of the children if Boo hadn't stepped in to save them. Dill's curiosity also shows Jem and Scout the realization that the gossip about Boo is false, and that it is just social prejudice showing us that Boo is a good man and friend. He teaches them Appearance vs. reality- a lesson that readers can benefit from too.