At the end right before Judge JBL delivers his decision The Miz delivers his surprise bit of evidence, the briefcase. That would not be allowed in a actual court case. The Federal Rules of Civil Procedure (which govern civil cases in the United States) require all parties disclose all evidence before trial in the discovery phase. So the briefcase would not be allowed. If it did happen in real life Otis would have an easy time appealing that decision.
When Asuka is speaking Japanese the Judge JBL asks if the court reporter (Teddy Long) is getting everything down and he says, yes. Court reporters in the United States are only allowed to take down the spoken word in the English Language. Therefore only English language testimony is allowed into evidence. If Asuka didn't know enough English a Japanese translator would need to be provided and the court reporter would take down only the translator's translations form the Japanese language to the English language.
When it is reveled that Teddy Long is the court reporter if you look at his screen on his computer there was no translations. You can tell he wasn't translating (preforming his job as a court reporter).