It goes down like this,
Maroni and his gang are captured during a montage around scene 90 of the movie and Maroni is finally able to go on trial.
Because it is MARONI who is on trial INSTEAD of Falcone in the film universe, Maroni would NOT testify against himself. Instead a henchman of his, Rossi, brings the acid to court and throws it in Harvey Dent's face.
It is still Maroni who is responsible, but he doesn't directly do it himself because he would obviously plead the fifth in a trial like this, and wouldn't do something to incriminate himself further - since he still GETS OUT.
It's because this happens around scene 160, and then Two Face re-emerges around 306 to try and get his revenge on Maroni.
During scenes 304,305,306 is when Two-Face flips his coin that ends up with him killing Maroni's driver, but sparring Maroni, he then blows the car up.
Joker is NOT involved in Dent's scarring in the film universe.
Thanks for the info.