The teacher told us that he would begin the dictionart when we were ready.这句话有语法错误吗

没有错误,when改不改成if都可以.
句子跟你的另一个提问有点像：Mr.Zhang would take the thief to the police when he met the man again.这个句子中“再次碰到那个人”是不确定的,所以when改为if意思上会比较好,表示假设；
而你这次的提问中,“我们准备好”是老师说完话后应该要发生的事,比较确定,所以用if或when都可以.