Nearly falling in the manhole (Dramatic Irony)
Much of the comedy in City Lights is predicated on instances of dramatic irony, in which the viewer knows something a character (usually the Tramp) does not. This first occurs when the Tramp is staring at the sculptures in the shop window, early in the film. Behind him is a manhole that keeps opening and closing. Unbeknownst to the Tramp, every time he walks backwards to get a better look at the sculptures, a cover comes over the manhole, preventing him from falling in, and then when he walks towards the window, the manhole opens up again. This creates dramatic irony in that, as we watch, we worry that he is going to fall in the hole, while he has no idea of the danger he is in.
An Unlikely Friendship (Situational/Dramatic Irony)
The friendship between the Millionaire and the Tramp is ironic in itself, because they are an unlikely pair. While the Tramp has no belongings or assets to his name, the Millionaire seems to have an endless supply of cash. Thus, their friendship and the fact that they are so mismatched based on class is ironic.
Additionally, the Millionaire's lapses in memory account for another instance of dramatic irony. When he sobers up, he has no memory of his friendship with the Tramp, and is confused by why such a vagrant is in his home. While we the viewer know that only a few hours ago he was professing lifelong loyalty to the Tramp, the Millionaire, because of his intoxicated blackouts, has no idea.
The Ending (Dramatic Irony)
At the end, the Flower Girl can finally see, and when she gets a glimpse of the Tramp on the street, she laughs at him and goes to piteously give him a flower. While we the viewer know that he is her benefactor and the man with whom she fell in love when she was blind, she does not know his identity and simply thinks he is a common tramp.
Wrongful Imprisonment (Dramatic Irony)
This bit of irony is akin to the dramatic irony of the Millionaire not knowing the Tramp's identity when he is sober. When the robbers assault the Millionaire and rush out of the house, the cops come and suspect that the Tramp is a thief and the man who assaulted the Millionaire. While we know that the Millionaire willingly gave the Tramp $1000 when he was drunk, he has no such recollection when being questioned by the police and so the police arrest the Tramp and put him in jail. Thus there is a discrepancy between what the Millionaire and the cops know and what the audience knows to be true.