All right, to try and clear this all up, POTO is not an opera because it does in fact have dialogue more than in Act I. Ex. Act II; scene II, scene IV, scene VI, not to mention in Act I -- scenes I-III.
As for what makes an opera an opera and a musical a musical has been said to be because an opera is almost always a drama which is completely or mostly sung. Opera is led mainly by the vocals and orchestra, whereas musicals are carried through by the dialogue.
But, the "rules" have changed after such operas as Carmen and The Daughter of Regiment with them featuring dialogue. But going back to the original topic, ALW's work, POTO is tricky, but just like Les Miserables, Sweeney Todd, they are musicals, not operas.
The reason being why operas are operas and musicals are musicals can no longer be because operas are dramatic and musicals tend to be comedies, because of musicals like POTO, Les Mis, and Sweeney Todd. Still, we can say POTO is not an opera because it proceeds to tell a story through dialogue; ex. Mme. Giry explaining to Raoul how the Phantom came to be.
Musicals tend to use dialogue to tell a story and add in song and dance to enhance the plot. Opera tells its story mainly through song.
Though again this could be debated with examples such as Carousel and Mozart's The Magic Flute, there ARE differences between operas and musicals.
Musical singers are usually miked, whereas opera singers are generally not.
Also, opera has been around for a heck of a lot longer, and let's not forget it's actually sung in a different language (all of it).
"More than in any other performing arts the lack of respect for acting seems to spring from the fact that every layman considers himself a valid critic."
--Uta Hagen