Q1: 

我買了貴出版社的 口譯大師跟讀課

第 12 頁有一句 " without my noticing it "

my 是否該更正為 me 呢 ? 

A1:

without MY noticing it

without ME noticing it

兩種用法皆可，供您參考。

Q2:

Track 02 page 16 of 口譯大師跟讀課
has the following sentence:
... which makes Friday my favorite day of a week.
shouldnt it be THE week ?

A2:

正確應為 of THE week，

我們會於再刷時更正。謝謝您！

謝謝 HC 的購買與建議，

以上將於書籍再刷時更正。
造成學習困擾，深感抱歉，特此公告。