"Which notes are incorrect"? Does it sound good to your ears?
First, lemme say I like the song. I mean, really. Had my foot tapping and head bobbing right away.
As for leads, you do the same thing countless players before you have done: Take those 2 John Petrucci albums, the Metallica album, and the other 2 you say are all you listen to, and learn some of the licks from those solos.
If you wanna understand theory, then start learning about it. Take lessons if it's that important to you. But plenty of great guitarist write killer solos, without knowing theory. They use their ears. But it doesn't hurt to check out guitar magazines, and read the articles that dissect tasty licks, and why they sound good over the chords underneath.
Then, you start incorporating licks from guitarists you like, and the stuff you learn from other sources, and begin putting it all together into your own solos.
I'm sure you've heard something Petrucci has done in a solo, that just grabbed you. Pull up the tab, and learn it, and rip it off! Do enough of that, from enough different players and sources, and change it around to make it different, or easier to play, mix it up, and spit it back out in your own way. If you mix up enough diverse sources, you should end up with solos that start to sound like YOU.
Good luck.
Also- This is a lifelong journey. Never stop crafting your style. Just look at what Paul Gilbert is doing these days.