Is the entire Bible read at mass? I'm not a Catholic, but I have attended Catholic Mass and I've been acquainted with the practice of regular mass- that a certain week of the year has the same readings each year.

Is the entirety of the Bible read throughout the year during mass? If not, what passages (or books) are never included?
The Revised Common Lectionary (by far the most common, used by Roman Catholics, Episcopalians, Methodists, and others) is a three year cycle, and if you attend every Sunday, you are guaranteed to hear selections from every book of the canon, but not necessarily the entirety of each book. 

That said, there are several texts you will hear repeated, either for their suitability to certain parts of the church year, or because of their relative importance. 

Finally, if you read the daily lectionary (a 2-year cycle), you will cover much more of the bible, but there will still be some parts (1 Chronicles 1-10, I'm looking at you!) that will still be missed. 

As a Baptist turned Episcopalian turned back Baptist, I can say that I was surprised at how much more Scripture one hears in a lectionary setting. It is a nice discipline, but it is not exactly the same as reading the Bible through in a year.