句子意思为:他们要考虑的最重要的问题之一就是有关公共卫生的问题.
通过分析句子成分可知:One of the most important questions they had to consider 为句子主语;____ of public health为句子表语.
由于was之后跟的并不是从句,所以应排除引导从句的连词what与which,
同时根据句意可知,空白处所填的词相当于the question.
此句可还原为:One of the most important questions they had to consider was the question of public health.
此时句子为了避免前后重复,the question应用适当的代词来代替.而代替单数可数名词,我们一般选用that或the one,表示同类中的特指.
所以本题应填that.