Dramatic irony, of course, is when the reader knows something that the character does not know. There are numerous examples of dramatic irony in To Kill a Mockingbird, but let me get you started with a few arranged in order of importance.
First, and probably the least significant but an example of dramatic irony just the same, is when Uncle Jack tells Scout a funny story as she fusses and frets about a big splinter under her skin. The readers know that Uncle Jack is trying to take her mind off of the pain, so that the splinter can be removed. However, that fact surprises Scout. The effect of this particular instance of dramatic irony is humor.
Second, there is the tense scene during which Scout asks about rape. The readers of the book all know exactly what rape is. Scout, being the innocent in To Kill a Mockinbird, does not. Therefore, this time Lee's use of dramatic irony creates a bit of suspense.
Third, there is the amazing scene where Atticus saves the town by shooting a rabid dog with one quick shot to the head. By the middle of the incident, as Heck Tate talks with Atticus, the audience knows that it is Atticus who is the best shot in town, but it isn't until the shot is fired that both Scout and Jem understand this. Not only does this create suspense, but also adds a lot to Atticus' characterization (proving that he is a brave enough man to keep a murderous skill like marksmanship to himself).
Finally, there is the scene when Scout shows up at the jail, showing great loyalty to Atticus. When Scout arrives, she immediately sees Mr. Cunningham and asks how his "entailment" is coming along. Mr. Cunningham, who has come to the jail to do possible injury to Atticus, is thrown off-guard by Scout's innocent and caring question. We understand this, but Scout does not. Scout, through dramatic irony, deflects the angry mob at the jail. The effect here is all suspense related.
Lee, then, is a master of dramatic irony, as it permiates the book and creates numerous effects with a single literary device.