shift in verb tense

1: An unnecessary shift in tense 【不该变却变】
错误:
He reads the newspaper and [noted] the sports scores.
=>
He reads the newspaper and notes the sports scores.

错误:
Nancy arrived just as the play [begins].
Nancy arrived just as the play began.

2：A lack of correct shift in tense. 【该变不变】
By the time the fire broke out, we were asleep for hours.
=>
By the time the fire broke out, we had been asleep for hours.
When we met for the first time, we knew each other's names.

=>
When we met for the first time, we had known each other's names.