If you have nothing but a video recording of the deceased person's last wishes, you're very unlikely to have a will that would hold up in court. Of course, if the relatives all agree to follow the recorded wishes, and debts and taxes are paid, then there's no problem with the family accepting a recorded statement as a sort of will. Just don't expect a probate court—or a bank or other institution that controls any assets in the deceased person's name—to accept it.
To be valid, a will must be in writing and signed. And in most cases, a will must also be dated and signed by two witnesses who watched the will maker sign it. A few states are beginning to allow electronic wills (or e-wills), but so far these electronic documents must be textual, and a video recording won't suffice.
If the person who made the will recorded the will-signing ceremony or read the will aloud on camera, this documentation could still be useful in some situations:
A relative is claiming that the will maker wasn't of sound mind when the will was signed. If a disappointed relative is making noises about contesting a written will in court, charging that the will maker didn't realize what he or she was doing or was being unduly influenced, evidence that the will maker was in fact lucid and rational is very helpful. Someone challenging a will must produce persuasive evidence that the will maker wasn't aware of his family and property or was being unduly influenced by someone hoping to profit. A recording of the will maker explaining his or her actions, or simply appearing to be acting freely, can help refute such charges.
Someone is claiming that the will wasn't executed properly. For a will to be valid, it must be signed with certain formalities. Generally, there must be two adult witnesses, and the will maker must tell them that the document is his or her final will. A recording could show that the witnesses watched the will maker sign and then signed the document themselves. That way, no one could claim that the will wasn't witnessed properly.
Relatives are upset or puzzled by provisions of the will. Most family arguments after a death are triggered by surprises. For example, if the children expected to receive equal shares of a parent's estate, but don't, hard feelings may follow. If the will maker left a recorded explanation, it can soothe ruffled feathers. If, for example, a parent explained that she was leaving more money to one of her children because she had already given the others money to help buy their own houses, it could help avert speculation about the parent's reasoning and disputes among the kids.
If you're an executor and you fear that relatives might mount a legal battle over the estate's assets, consult a probate attorney immediately. An experienced lawyer may be able to suggest creative steps that you can take to head off a fight—for example, proposing a compromise or holding a session with a professional mediator who can help family members reach an agreement.