Since Harlan Thrombey is not married at the time of his death, his children (Walt and Linda, but not Toni, who is his daughter-in-law) are entitled to some of the personal effects from the estate. Section 2-403 of the Massachusetts Uniform Probate Code:
The decedent's surviving spouse is entitled from the estate to a value at date of death, not exceeding $10,000 in excess of any security interests therein, in household furniture, automobiles, furnishings, appliances, and personal effects. If there is no surviving spouse, the decedent's children are entitled jointly to the same value. ... These rights are in addition to any benefit or share passing to the surviving spouse or children by the decedent's will, unless otherwise provided, by intestate succession, or by way of elective share.
This means that even if the will held up in probate court, Marta would probably still not be entitled to "the house ... and all belongings therein"; Walt and Linda would get to pick out up to $10,000 (between them) of their favorite pieces. To be honest, though, you could probably remove $10,000 worth of furniture from that house and it would look largely the same. And, of course, the house itself, the money, and the business are not affected by this clause.
Note that unlike surviving children, a surviving spouse cannot be completely disinherited under Massachusetts law. A surviving spouse can choose the "elective share" of the estate instead:
The surviving husband or wife of a deceased person, except as provided in section thirty-six of chapter two hundred and nine, within six months after the probate of the will of such deceased, may file in the registry of probate a writing signed by him or by her, waiving any provisions that may have been made in it for him or for her, or claiming such portion of the estate of the deceased as he or she is given the right to claim under this section, and if the deceased left issue, he or she shall thereupon take one third of the personal and one third of the real property; ... if he or she would thus take real and personal property to an amount exceeding twenty-five thousand dollars in value, he or she shall receive, in addition to that amount, only the income during his or her life of the excess of his or her share of such estate above that amount, the personal property to be held in trust and the real property vested in him or her for life, from the death of the deceased. ...
If I'm reading this correctly, this means that if Harlan's wife (or husband?) had still been alive during the movie, and had been disinherited in the will as the children were, she could have claimed $25,000 outright and a life interest in one-third of the estate (less the $25,000.) Given the ongoing income from the publishing business, this would probably have been quite lucrative. However, there do not appear to be similar provisions for Walt and Linda under Massachusetts law.