In Pokémon X and Y, the Judge is an Ace Trainer located in the Kiloude City Pokémon Center. In Pokémon Omega Ruby and Alpha Sapphire, he is located in the Battle Resort Pokémon Center. In addition to noting the overall total and highest IV of a Pokémon, he will make special comments if the Pokémon shown to him has an IV of 0 in any of its stats. The number of times Pokémon were judged by him are shown during Link Battles.
"You can call me the Judge. Heh heh, that's actually not my real name, but it's what everyone calls me. It's because of this weird power I have. It's a gift, really. I can discern--or judge, you might say--the overall potential of individual Pokémon. How about it? Let me judge the intriguing potential of your Pokémon!"
"Hey there! So how about it? Are you gonna let me judge the intriguing potential of your Pokémon?"
After selecting a Pokémon
"I see... I see.."
"This Pokémon's potential is <Pokémon's potential> overall."
"That's how I judge it, anyway."
Highest individual stat
"Incidentally, I would say its greatest potential lies in its "
(If the Pokémon has two or more equally good best stats, then he will add one of the following lines:)
"But its Attack stat is good, too."
"Hmm. And its Defense stat is good, too."
"Although its Sp. Atk stat is equally good."
"Its Sp. Def stat seems just as good, though."
"And, well, its Speed stat is good, too."
To describe the value of the Pokémon's highest IV(s), he will use one of the following lines:
IV range of 0-15: "It has rather decent stats, I'd say. That's how I judge it."
IV range of 16-25: "It's definitely got some good stats. That's how I judge it."
IV range 26-30: "This Pokémon has some fantastic stats. That's how I judge it."
IV of 31: "Stats like those... They simply can't be beat! That's how I judge it."
Lowest individual stat
If a Pokémon has any IV of 0, he will use one of the following lines:
"But its HP... It's pretty dismal, you know?"
"But this Attack stat... It's terrible..."
"But how can you make it through battle with this kind of Defense stat?"
"But this Sp. Atk won't even leave a scratch on an opponent..."
"But this low of a Sp. Def stat is going to leave you high and dry..."
"But you won't get anywhere fast with this low of a Speed stat..."
(And if there are 2 or more IVs of 0, then he will also use one of the following lines:)
"And that's quite a disappointing Attack stat there, isn't it?"
"And that Defense stat is nothing to write home about, you know?"
"And I'm afraid that its Sp. Atk is pretty bad, too..."
"And it looks like it's no great shakes when it comes to Sp. Def either..."
"And that Speed stat... Well, it's nothing to brag about, that's for sure."
In the rare event that all six of the Pokémon's IVs are 0, then he will describe how all its stats are its best stats, and then describe how all of them are bad.
Hope I helped!