Jenny's Abuse (Dramatic Irony)
There are moments in which Forrest's intellectual limitations cause him to have a different perception from the viewer. For instance, adult Forrest recalls that Jenny’s father was a “lovin’ man, always kissing and hugging her and her sisters," which the viewer knows to mean that he molested Jenny. There is a disturbing disconnect between what Forrest understands and what we the viewer see to be true.
She was a folk singer (Dramatic Irony)
Another instance of dramatic irony occurs when Forrest goes to see Jenny perform in Memphis. She is in a strip club, naked and playing "Blowin' in the Wind" by Bob Dylan to a room full of disrespectful men, but Forrest sees her and is sure that her dream has finally come true and she is a real folk singer. The viewer knows that she is far from a real folk singer, but Forrest's limitations cause him to misperceive the scenario as a legitimate "big break."
Your Son is Different (Situational Irony)
Early on in the film, we see Mrs. Gump telling Forrest that no matter what anyone says, he must know that he is no different than anyone else. No sooner has she said this than the scene shifts to the public school principal's office as he tells Mrs. Gump point blank, "Your son is different." Director Robert Zemeckis shows the irony of Mrs. Gump telling her son that he is just like everybody else, when actually everyone is constantly reminding him that he is different.
Vietnam Veterans Against the War (Dramatic and Situational Irony)
Forrest finds himself in many ironic situations, but perhaps the most ironic one is when, immediately after receiving a medal of honor from the president for his service in Vietnam, he gets pulled into a line of veterans who are on their way to a rally protesting the war. Once there, he is asked to address the crowd, but the sound goes out during his speech, so no one can hear what he has to say. In this instance, there is dramatic irony, because we the viewer know that Forrest does not have a political critique of the war like the hippies who are holding the rally, but they hold him up as their hero, because they assume he shares their beliefs. It is also, in a broader sense, highly situationally ironic that Forrest ends up as a hero on two ends of the political spectrum in one day.