If you look closely during this part, you can even see "laceration, evisceration, incineration" there at the bottom!
The Book: There is no contract. At least, there's nothing that Bilbo is required to read, understand, and sign. The note that Thorin leaves on Bilbo's mantelpiece has some attributes of a contract, however. It is as follows:
"Thorin and Company to Burglar Bilbo greetings! For your hospitality our sincerest thanks, and for your offer of professional assistance our grateful acceptance. Terms: cash on delivery, up to and not exceeding one fourteenth of total profits (if any); all travelling expenses guaranteed in any event; funeral expenses to be defrayed by us or our representatives, if occasion arises and the matter is not otherwise arranged for.
Thinking it unnecessary to disturb your esteemed repose, we have proceeded in advance to make requisite preparations, and shall await your respected person at the Green Dragon Inn, Bywater, at 11 a.m. sharp. Trusting you will be punctual.
We have the honor to remain
Thorin & Co."
What does it matter? The contents of the contract are the same in the movie and the book - most of what's included in the book's "contract" is stated aloud. In either case, the contract is never given any serious importance in the book, and very minor importance in the movie. It is an insignificant change.
My Opinion: Like I said earlier, the document in the book isn't a contract at all. At least, not a legally binding one (not according to U.S. law, at least... but what do I know about Middle Earth's statutes and precedents?). I like it's inclusion, though. It adds some depth to the dwarves, especially Balin, who seems to have been the one to have written it. It breathes a little humor into the movie, especially the section that details various ways to die by dragon (in rhyme!)
If you're interested in seeing what Dwarf Legalese looks like, by the way, the contract has been transcribed in whole by a much greater fan than I.