If he wasn't diagnosed with Antisocial PD, he will be now. As far as schizophrenia, I'm leaning to no. Individuals with schizophrenia tend to lose the ability to organize their behavior. They also have difficulty performing the tasks of everyday living. Holmes was very organized and self controlled.
bear with me: 2 mass shooters here in my country were extremely organized, one went to medical school and planed his shooting 7 years ahead (he dreamt about it and the idea grew stronger everyday until the day he couldn't bear the urge anymore and had to commit the crime). He did lot of serious planning yet the guy was on and off antipsychotics, later was diagnosed schizophrenic. The other mass shooter went to college, had a nice job and would go to work everyday, he was never ever late, very organized and serious, yet he planned an uncredible mass shooting, he left a manifesto, youtube videos, even a letter of how he wanted to be buried, he learned how to shoot and got weapons illegally in the black market, he fooled everyone, family friends, doctors, co-workers. Aftermath: he killed 12 innocent kids but his revenge was because in his mind he was killing the children that bullied him in the past when he was at school, the psychiatrist said after reading his letters with his motives that probably when this killer entered the school and fired at random kids, he didn't see innocent strangers, he just saw his bullies and his mind they deserved to die. His biological mother was schizophrenic, but he was adopted and didn't know about his real mom. Both shooters were 24 years old, both schizophrenics on and off medication, both intelligent and pretty damn organized, normal families, middle and upper class, we have security guards with bullet proof vests and weapons almost everywhere we go, from schools to shopping malls, yet nobody could stop and avoid those shootings, they were going to psychiatrist, on and off meds, yet nothing could be done. Those things are hard to predict.
Premeditation, being organized, self controled IMHO does not rule out schizophrenia. Delusions can be long-term, some schizophrenics might think "I'm Elvis today", while some might believe they are Elvis for months or years at a time. I'm not excusing what JH did by any means, just pointing out that consistent planning actions would make sense if he believed himself to be the Joker.
Mind you, I'm not saying he is schizophrenic, I know nobody want to consider this possibility also I don't have the expertise to diagnose him (I need to make this disclaimer, before someone here shoot me and nag about what media says that there is no proof the guy is mentally ill, yadayada, yes I know that) I just want to point out that things aren't black and white, being organized and self controlled doesn't mean much sometimes,2 mass shooters in my country were schizophrenics, both were very good at hiding things. This is why I wouldn't be so sure to say that he is not schizophrenic just because the guy, studied neuroscience, planned so carefully, was highly organized and performed the tasks of his everyday living. You can be a lunatic and still fool everyone for a while until something horrific happens that will make people notice that something is wrong.