I've heard that some publishing companies hire people (paying them in books) to read manuscripts and give their opinions of the books. Is this true? If so, how do I get hired doing this?
Yes, many publishing companies do this. I'm not sure how you go about getting hired to do this. You can always call them up and ask, but I'm not sure if that will help much. This is probably one of those things where you have to know someone--or rather, they have to know you. In my company, these positions are offered by me, after I've known someone for awhile and we've discussed various books a lot, and I know that I can trust their assessment of a book.
If you really want to do this, but you don't have the personal connections, you might offer to read a few on spec, so they can see if you're a good match for their company.
Habits and/or Skills that would impress me:
Read a lot of books--I'm talking 80 to 100 per year, year after year; you need to be able to recognize current trends and when something has been done to death
Read in a lot of genres--know the various conventions used, needed, expected in each genre; be able to talk/write about them intelligently
Basic grammar/editing skills--you need to recognize when something is written properly and when it is not; whether it needs only light editing or heavy editing
Basic writing skills--you need to be able to recognize certain writing styles, techniques, and discuss them using correct terminology (ex: POV, etc.); you also need to be able to clearly express what worked in a book, and what didn't, and why
Picky, picky, picky--If you read a lot of books, and you like most of them, you're probably not discriminating enough. On the other hand, if you hate everything you read, that's probably not going to work either.