Dio is just as charming onset as he is offset. He has natural charisma. However, he is a pretty decent person when not in character. Unlike Jonathan though, he spends a lot of time in the makeup tent to get the special effects makeup and his hair right. He and Kars have had a lot of talks during this time.
"It takes a long time to look this much like a fabulous bastard." -Dio at some point.

He does screech his 'wryy' when upset. Like when old Joseph flubs his lines. He has had his own line mistakes though so he is not too harsh.

Giorno and the other 'brando bunch' are his real sons and he is proud of them. He greets them everyday on set and tells them how proud he is of them.
He and Giorno both wryy when they are startled by pranks done by Esidisi.
Dio apologized to Danny after having to kick him. He did not like the idea of hurting the dog.

When visiting the local hospital with the others, he keeps in character. Turns on the charm but turns down the assholery. He's popular with edgy teen boys and women.
He and Vanilla ice do have a close friendship offset. They do cleanup after shooting is over and Ice has watched over Dio's sons when they were sick when Dio was busy.

Like Jonathan, he is hard to make costumes for. But for Prosciutto, it was the pure absurdity of the decoration that drove the designer to despise making costumes for him. Prosciutto just accepted after the first three outfits and got Suzie Q for help.
Dio is a little uncomfortable with the clothes but his boldness allowed him to get over that easy, plus having Kars and the others wearing less was good distraction. 
He hates the shoes though.

Dio and Diavolo get along during their breaks, they talk about their children and how proud of them they are. This usually gets the Brando boys, Trish and Doppio kind of embarrassed by having their fathers talk about them.

He is not very phased by bloopers and has some of the best by far.
He just plays along with any bloopers that may happen and create comedy gold from doing so. The cast and crew always go into an uproar after he does this.
Dio may be a comedy genius but he does have concern for his fellow crewmembers, he went to see if Polnareff was okay after he tripped on that stair scene.

Dio and the actor that plays The World get along well. They sometimes do silly dances to lighten the mood after a bad day. The other stand actors tend to join in during this.

BLOOPERS:

As stated before he has the best and most humorous bloopers.
The most memorable one when he forgot his line goes as follows:

Dio: As such I have lost the ability to... Fuck. It really does not want to work.
(The crew is laughing)
Enyaba: you lost the ability to fuck, my lord?
Dio: Yes I have. Ice, can you go down to the corner store and get something for me? Like a Viagra or something?
Ice: Yes lord Dio.