He was too emotional. When everything was fine, he smiled all the time and made everyone feel good. But when things weren't going his way, he took it personally and sulked. And he made everyone feel miserable. He probably wasn't too good at dealing with criticism and personal animosity. Too emo, too vulnerable. It's very un-NHL or unprofessional in general. Guys who do annoyed faces in certain situations usually take the bus to a farm team quickly. But Jagr was too good.
He was reluctant to help with defense. He was not a floater, but when a situation called for it, most of the time, all he could do in his own end was a half-arsed hook attempt that often resulted in a penalty. It was frustrating to watch, because he sometimes took too long to help out, hoping his mates would just get it done, and also because he actually could strip people off the puck nice and clean just using his strength, but unless it was to happen close to the net it was desirable to score on, he would rather not try.
He had no grit, which often comes along with clutch, but it is not the same thing. Jagr was clutch, but he wasn't gritty. He was not one of the guys who suddenly do no wrong and slide on their butts for the good of the team. He could step it up, but you felt there always was a superstar restraint. Except for the 99 Devils playoff. He did go out of his way there.
He did get kinda big-headed near the end of his Pittsburgh tenure. It was in the air. I think it gets overblown, but it was there.
He could be a somewhat cruel joker/prankster. Jagr jokes a lot, and that's good. But he used to frequently cross the line into the near-bully zone according to current sensibilities. I remember watching an interview with his personal coach who remembered "a good one".
He had a colleague who came for a stint in Pittsburgh. Generous as he sometimes was, Jagr took them out for dinner in a fancy restaurant. And as the poor, no-English colleague took a restroom break, Jagr stuffed his jacket full of silver knives and forks... When the guy came back, he found their table and his jacket surrounded by the staff, with raised eyebrows. And as they began to take the silverware out of his pockets, he stammered "this can't be, I did not, I could not... This is a mistake. Jaromir, say something!"
And Jaromir did. "I don't even know this guy."
They called the cops. Since the guy couldn't explain anything at all, they just threw him in the car, tomato-red, and drove him away. They drove him a good two hundred meters before letting the poor folk out, pale white, stumbling. You can guess what Jagr was doing. Even the reporter hearing the story cracked up, but it must have been no fun being put through this for amusement of a bored, wealthy, superstar jock. You can guess if he just used people for fun like this, at least some of them didn't like it. If stuff like this happened these days and it went public, Jagr would be risking the politically non-desirable territory.