1. Regarding jim's guess at the Christmas party that bill has deteriorated, I feel that this is the author's subjective assumption. If jim guesses that bill has gone bad, the boss's action to send him to Budapest is not valid. If it is to confirm his guess, he will never show the slightest strangeness in his interactions with the other party. This kind of old agent won't guess who is undercover unless he has absolute evidence, which is obviously unprofessional.
2. Regarding the night Jim was killed, Bill was at Smiley's house. The movie is not obscure. Smiley directly said in his conversation with Peter that Bill was at his house at that time.
3. Regarding Bill's notification to Karla not to kill Jim, this is contradictory to the plot and cannot stand scrutiny. If karla was going to kill jim, it would never be with such a crappy shooter. And on the spot, the other party's organizer also ran out and shouted not to kill him. And since this is a trap set up by Karla, it is necessary to capture Jim alive, or to bring wrong information. But this trap is too fake to deceive people. So Jim finds out something is wrong and leaves right away and gets shot.
4. The fact that jim was rescued and tortured proved the above. But jim's face shot irina, which the movie did describe, but in the 1979 Alec Guinness version of "ttss", irina's death came from intelligence, not jim's own eyes.
5. About smiley recalled that he ran into Bill when he came home from Berlin that day, and deduced that he had just had sex with his wife, which is obviously the wrong time. Smiley did bump into Bill when he came home from Berlin, but not the day Jim happened or the next morning. The reason is that Bill immediately rushed to the headquarters to direct the aftermath after listening to Jerry's call. How could he return to Smiley's house and pretend to be in such a hurry? The time for this "rape" is obviously a few days later, not at the time mentioned.
6. The story does not describe why Jim shot Bill. I guess jim has been instigated by karla. The time was right after he was shot and he was the soldier karla dealt with after the potential exposure of the bill.
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