Sigh. Always the lawyers!
The legal-minded Bilbo, member of a race which required seven signatures in red ink of witnesses to a will, surely had not forgotten the terms of the contract, and was likely well aware of its lack of detail in some points. Good think the Dwarves didn't think to have Messrs Grubb, Grubb, and Burrowes draw it up. Then again, maybe Gandalf planned it that way.
At any rate, my thought is the Judge, Gandalf, delivered his opinion of it, favorable to Mr. Baggins. Thorin may appeal to the 10th Appeals Court of Orthanc.