Nah, didn't think the mustache fit him that nicely. Thankfully they did take it off quickly.
My problem stems more with Goku and Vegeta, notably the two most important characters. Goku's naive nature and idiocy seems to have been exaggerated by the people in charge of it, in both the manga and the anime. Goku was naive before, granted, but his naivete seemed to come more from social awkwardness, not from flat out idiocy. To name a few examples we have Goku constantly making silly remarks, not understanding the other's explanations and needing Vegeta to get such in his thick head, not knowing what a kiss means despite having already had 2 child's, forgetting Zamasu's seal and initially not caring that his desire of setting an universal tournament could mean the end of several billions of people. Plus, he stating that he doesn't seem fit to train Oob and needing to be encouraged by Dende to take such task doesn't feel right. Never got the impression that Goku was initially against the idea of training Boo's reincarnation.
On Vegeta's side, we have him still feeding his old rivalry with Goku, stating he can't get around the fact that he's always the second, while... That come off as strange given this latter's admittance of inferiority to Goku, in which he understood Goku was simply better than him and the WHY he couldn't surpass him despite all his heavy training. So a Vegeta that screams to his lungs on how he must surpass Kakarotto doesn't feel right to me. I prefer the way he was handled in GT, with such thought no longer being a recurring theme.
As for side characters like Piccolo, Gohan, Kuririn... While it'd be nice to give the first two more of a role in the story, I don't think their characterisation were necessarily handled out poorly. Gohan is doing what he always wished -- studying -- and Piccolo seems to be kept consistent with how he was dealt -- except maybe the moment in the u6 Tournament of the manga in which he claims to be Piccolo's evil reincarnation... While he seemed to have abandoned such title post fusing with Kami, by proclaiming himself to be a "Namekian who has forgotten his own name".