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.