What do you think is the best film of the year?= What is the best film of the year?(你觉得)今年最好的电影是哪一部?
do you think 是插入语,可以理解为一个语气词,不影响句子成分,可以省去.
What did you say his name was?你说他的名字是什么来着?是对"You said his name was ..."这句话的提问.did you say 在这里有实际意义,不可以省去."his name was" 是say的宾语,在疑问句型中仍保持陈述句式,was不可以前置.