In The Westing Game, why might Judge Ford want to kill Sam Westing?

Judge Ford owes Sam Westing money she can’t afford to pay back. 

When Sandy McSouthers tells Judge Ford that there is smoke coming from the Westing house, she has a strong reaction.  He asks her if she believes in ghosts, and then tells her he is repeating what Otis Amber said.  She tells him Otis Amber is a stupid man, and immediately regrets it.  The comment was made because she is worried that Westing really was back. 

So Sam Westing has come home at last. Well, she could sell the car, take out a bank loan, pay him back—in cash. But would he take it? (Ch. 3) 

Grace Wexler wonders why Judge Ford is there.  She is a black woman, so Grace doesn't think she is a Westing heir since Westing was not black.  She decides the judge must be there in “in some legal capacity.”  She gets upset when the will is read and Westing refers to them all as nieces and nephews. 

Judge Ford does not like Sam Westing.  She says he was crazy when she finds out about the game and is insulted by the whole script.  She feels like it is another cruel trick of Sam Westing.  She says she will play the game as he would have played it—mean. 

The debt that Judge Ford speaks of is Westing paying for her education at Columbia and Harvard.  Her parents worked for Sam Westing as a maid and a gardener.  She used to play chess with Sam Westing, who constantly insulted her and won every game.  However, he sent her to boarding school, college, and law school.  He made sure that she got into the best schools.  She believed he did it because it was “to Sam Westing’s advantage to have a judge in his debt.”  

When she said all of this to Sandy McSouthers, who is actually Sam Westing, his response hints at the reason he might have paid for her education. 

“You’re awfully hard on yourself, judge. And on him. Maybe Westing paid for your education ‘cause you were smart and needy, and you did all the rest by yourself. (Ch. 21) 

Sam Westing may have insulted J.J. Ford, but he also saw something in her from a young age.  He taught her chess, and knew she was smart.  He paid for her education because he felt that she deserved it, and not because he wanted something from her.  As her presence in the game shows, he considered her family.

In The Westing Game, what does Judge Ford believe Sam Westing is plotting against and why?

A reader should look to the second half of chapter 20 for this answer. Judge Ford and Sandy are continuing their questioning of game players in order to find out more background information about everybody involved. During this chapter, Ford is questioning George Theodorakis about his relationship with Violet Westing. Theodorakis explains that they were sweethearts, but he didn't have the money or fame to impress Mrs. Westing. Mrs. Westing forced the relationship to end and forced a new relationship on her daughter with some politician. Violet couldn't handle the situation and killed herself. Ford begins to put the pieces together, and she believes that Sam Westing is using this game to punish Mrs. Westing. Sam Westing believes that his former wife is to blame for Violet's death more than any other person, so he is plotting against her. This realization causes Ford to surmise that Mrs. Westing is one of the current heirs.

"We must not allow ourselves to be distracted from the real issue: Which heir did Sam Westing want punished?”

“The person who hurt him most?” Sandy guessed.

“And who would that be?”

“The person who caused his daughter’s death?”

“Exactly, Mr. McSouthers. Sam Westing plotted against the person he held responsible for his daughter’s suicide, the person who forced Violet Westing to marry a man she loathed.”

“Mrs. Westing? But that’s not possible, judge. Mrs. Westing is not one of the heirs.”

“I think she is, Mr. McSouthers. The former wife of Sam Westing must be one of the heirs. Mrs. Westing is the answer, and whoever she is, she is the one we have to protect.”

What was Sam Westing's big mistake according to Judge Ford in The Westing Game?

Sam Westing's mistake, according Judge Ford, was including an incorrect heir. (Raskin 120)  Sydelle Pulaski, the secretary to the president of Shultz Sausages, was chosen to live in Sunset Towers.  The correct heir (a friend of his ex-wife in her youth) was a woman named Sybil Pulaski.  This error, however, is not of huge consequence, as all the heirs end up receiving the same amount of money, and the correct woman, Sybil Pulaski, is not included in this novel.  Sam Westing chose Otis Amber, a private investigator masquerading as a delivery "boy" to find most of the heirs, and the error regarding Ms Pulaski was his.

Source: Raskin, Ellen.  The Westing Game. New York: Avon Books, 1978.