I have heard that Shi'ite's believe the Prophet and some of his descendants to be "sinless"...?

I'll give a paraphrase of an answer provided by an Islamic scholar (Murtaza Mutahhari). Ismah (sinlessness) depends upon (iman) faith (in the Islamic sense, not in the sense of uncomphrending, blind belief) and understanding. Now, we could say that it is a sin to jump into a fire and so destroy your life. We don't commit such an act because we have full knowledge of the danger of such an act.

Muslims accept certain acts prohibited by Islam to be sinful and so refrain from them. For example, since Islam has forbidden alcohol and gambling, we refrain from them since we know that the harm that is in these things is greater than the good in them. But the risk these sins involve is not as clear as the risk involved in jumping into a fire. If we were as convinced of the harm of these sins as the harm of entering a fire, we would be "masoom" (sinless) as far as these particular sins were considered. The extent of a persons sinlessness, then, depends upon the extent of his faith and knowledge. The scope of the "protection" afforded one from his sins, depends upon the degree of the perfection of his faith - it depends upon the degree to which he has purified his "self"(nafs) and the degree to which he comphrends realities and partakes of knowledge.

"Prosperous is he who purifies it(his nafs) and failed is he who corrupts it" (Qur'an 9:7 -10)

Now, according to Islamic belief, the extent of the faith (iman) and knowledge of the Prophet(s.a.) is that of one who recieves revelation directly from God - whose iman(faith) is based on the certainty and experience of the metaphysical realities spoken of in the Qur'an and whose knowledge flows directly from God.

When someone reaches to this stage, they see the realities behind existing things, and the difference between that which is harmful (sinful) and beneficial is piercingly clear to them. When they are aware of the true realities behind existence, they refrain from what is sinful in the same way that an ordinary person refrains from throwing himself into a fire that would destroy him. They are purified from sin. The Qur'an says:

"Except Thy servants Amongst them, sincere and purified (by Thy grace)" (Qur'an 38:83)

As the Qur'an says, they achieve the highest stages of nearness to God, the highest Grace.

"And some who are, by Allahs leave, Foremost in good; Highest in Grace." (Qur'an 35:32)

They have the quality of Ismah, protection granted them by God (through perfect faith and knowledge) as a blessing for their efforts. The Qur'an mentions that, to these people, a special protection is available:

"He makes a guard to march before him and after him...." (72:26-28)

For more information on this subject, I refer you to the works of Mutahhari, Tabatabai, and other Shi'ite scholars.