1. We should judge a person not only by what he says but also his deeds.
此句中的what he said和his deeds在结构上是不平行的，因此其中一个应该被改正。即：
We should judge a person not only by what he says but also by what he does.(从句的平行)或We should judge a person not only by his words but also his deeds. (名词短语的平行)
2. We thought she was young, fair and a beautiful girl.
此句要么用名词短语的平行，要么用形容词短语的平行。即改为：We thought she was young, fair and beautiful.或We thought she was a young, fair and beautiful girl.
3. He sat down at the table and began to read newspaper. (动词短语的平行)
4. He likes playing basketball and collecting stamps. (非谓语动词的平行)
5. The teachers and students have great faith and high hopes for you.
此句中的名词faith和hope尽管是平行的，但它们应该接不同的介词。该为：The teachers and students have great faith in and high hopes for you.