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Before you even start, when you ask the interpreter for his/her name also ask for the certification number.
At least in CA, only a certified interpreter can interpret at a deposition.
If the interpreter is not certified raise the issue with the hiring party.
I'm not sure this is true. I've had plenty of interpreters who aren't certifying translating depositions in California.
And the other thing when they use third person, it sounds more like they're paraphrasing and not interpreting exactly what the witness is saying, so it definitely belongs in the colloquy format.
I agree with Kyung. In California I'm pretty sure they can stipulate to use whoever they want as an interpreter. Unfortunately for us, it makes it much hard when it is a relative with a very heavy accent. And for some languages and dialects you can't always find an interpeter. I absolutely love simultaneous translation.
I still remember a highly technical string of depos I had years ago where there was one interpreter, then each side had their "check interpreter" to make sure everything got translated right. Luckily they were all very cordial and professional. At breaks all three interpreters would discuss what were the best words to use. The worst part was I was lucky to get 100 pages per day with all the off the record discussions.