Francis Goes to Westpoint (1952)
Peter Sterling (Donald O'Connor) is a somewhat slow witted guy who is helped along by a talking mule. Calling Francis helpful might be putting it a little bit optimistically, actually, since the mule also gets him into loads of trouble. The latest being his acceptance into West Point Academy.
Peter Sterling has landed a job at the Fairview Atomic Plant. He's happy in his position but his luck is about to change when Francis tips him off on a ploy to blow up the factory. Peter informs the police and the FBI shows up, too. Nothing happens. The law-enforcement officials retreat, but not before getting the identity of Sterling's informant out of him. They're not happy when he blurts out that he's communicating with a mule.
A few minutes later a truck loaded with water bottles drives up to the gate. Francis alerts Sterling to look out for the people in the truck. It turns out some of the bottles contain liquid explosives. Sterling at once finds himself redeemed and his confession involving speaking animals is explained away by assuming he wants to protect his sources. The police, FBI and the military now vie for him to join their ranks. When he is offered a place at West Point, he can't resist the temptation.
After a few weeks he is called into the Academy Commander's (Les Tremayne) office because his academic record leaves much to be desired. He is 618th in his class of 618 cadets. If he isn't improving his results, he is informed, he'll be dropped from West Point. Good thing Francis is at hand to tutor him and gradually Peter's performance in school turns from unacceptable to outstanding. Still, he's understanding only half of what Francis crams into him.
Francis managed to follow Peter into West Point by covering for his cousin, who is the football team's mascot, and steers him through his first year all right. At a dance the cadets dress Francis up in the mascots garb and have a little fun with him, making him the lead in a polonaise. Peter intervenes because he feels his friend is being demeaned by this. He is ordered by an attending superior to explain his reasons for denying his fellow students a little bit of harmless fun, which results in him being punished by walking the grounds, something he already has ample experience in.
Winter turns into spring and then summer. The Army faces off the Navy at football. They're falling back and that is when Francis steps in to offer advice to the Army coach (Otto Hulett). The Army team rushes from victory to victory from then on. Their success comes at a price, though. Heading straight towards a nervous breakdown because at one point he no longer can bear listening to disembodied voices, the coach contemplates getting admitted into a mental institution. He tells the Academy's Commander about his troubles, who remembers something about a cadet telling him an equally fantastic story. He gets Sterling and together they pay Francis a visit to remedy the situation.
Well into his second year one of Peter's roommates gets news that his secretly married sister is having a baby and is too afraid to tell their father by herself. Because of a misunderstanding the Commander believes one of the three roommates is the expectant father and Sterling is ordered to give away the person's identity. Not knowing more than his superior about the situation, he refuses to rent his friend out, especially not after Francis told him how instrumental he is in winning the next football game. This leads to him being expelled. In the end, Francis can set matters straight, but Peter won't return to West Point.
Now, Where Does Leonard Nimoy Come Into Play?
A good point. He has a very small part as one of the football players (see that very badass guy with the #52 shirt?), appearing briefly in a few scenes in the locker room, and again in two scenes where he and a fellow player catch the coach talking to the mule, wondering if the coach has lost it. (Loads of screencaps here.)