1,John said his mother would buy him a five-speeds racing bicycle for his sixteenth birthday.
像five-speeds这种数词+名词构成的合成词或词组作另一个名词的定语是,只能用单数形式,所以要改为：five-speed racing bicycle
2,By reading the directions carefully,some mistakes in the examination could have been avoided.
此题中的could have been avoided是虚拟语气,而本句所表达的意思并非与事实相反,by...表示“通过...方法”,那么其后的“避免”是一个必然的事实,因此应改为：could be avoided,
3,I can't help to think it would be fun to play such an exciting game with them.
can't help（禁不住）后面的非谓语动词宾语要求动名词,应改为can't help thinking
4,Of the tew lectures,the first was by far the best one ,partly because the person who delivered it had such a pleasant voice.
既然是two lectures,就只能用比较级,所以by far the best one 中的the best应该为better.
5,The chairman proposed that every speaker must limit himself to fifteen minutes.
本句表示主语（The chairman）的愿望,因此后面的宾语从句要用虚拟语气,因此must limit 应该把must去掉.
6,When I got to the cinema ,the film had already started;I ought to get there earlier.
I ought to get there earlier是前面句子并列的主句,时态应保持一致,因此应该是I ought to have got there earlier.
7,After criticizing our proposal in every detail,the director went on telling us that there was nothing personal in his comments.
criticizing our proposal 与telling us 时两件相接的不同话题,而go on doing表示的是继续同一个话题,因此应该是go on to tell,即接下来继续另一个话题.