To spot pursuers and throw them off in a way that would appear accidental, was known as “dry-cleaning” (“proverka” in Russian), in intelligence parlance. To spot pursuers and throw them off in a way that would appear accidental, was known as “dry-cleaning” (“proverka” in Russian) in intelligence parlance.

Tohe act of spotting pursuers and throwing them off in a way that would appear accidental, wa is known as “dry-cleaning” (“proverka” in Russian), in intelligence parlance. The act of spotting pursuers and throwing them off in a way that would appear accidental is known as “dry-cleaning” (“proverka” in Russian), in intelligence parlance.

Since a target who was obviously under close watch was likely to be a trained intelligence operative, their demeanour must not arouse suspicion. Since a target who was obviously under close watch was likely to be a trained intelligence operative, their demeanour must not arouse suspicion.

This is a little unclear to me. Whose demeanour is referred to here? The target's? And what do you mean "obviously under close watch"? Obvious to whom?

Since a target who was obviously under close watch was likely to be a trained intelligence operative, their demeanour must not arouse suspicion. Since a target under close watch was likely to be a trained intelligence operative, their demeanour must not arouse suspicion.

As a KGB trainee, Oleg would learned how to set up a "signal site", how to make a “brush contact” and how to make a “dead-letter drop”. As a KGB trainee, Oleg learned how to set up a "signal site", how to make a “brush contact” and how to make a “dead-letter drop”.

I am not sure about this, but it seems awkward to use "would learn" here while the rest of the text is in past tense

As a KGB trainee, Oleg would learn how to set up a "signal site"," how to make a “brush contact,” and how to make a “dead-letter drop”.” As a KGB trainee, Oleg would learn how to set up a "signal site," how to make a “brush contact,” and how to make a “dead-letter drop.”

A "signal site" consisted in leaving a secret sign in a public place that meants nothing to a casual observer, but would convey to a spy a rendezvous to a spy. A "signal site" consisted in leaving a secret sign in a public place that means nothing to a casual observer, but would convey a rendezvous to a spy.

A "signal site" consisted inof leaving a secret sign in a public place that meant nothing to a casual observer, but would convey to a spy a rendezvous message to a spy. A "signal site" consisted of leaving a secret sign in a public place that meant nothing to a casual observer, but would convey a rendezvous message to a spy.

"Consisted of" is the correct phrase. :)

A “brush contact” consisted inwas the ability to physically passing a message or item to another person without being spotted. A “brush contact” was the ability to physically pass a message or item to another person without being spotted.

A “dead-drop letter” consisted inof leaving a message or cash at a given spot to be picked up by another without making direct contact. A “dead-drop letter” consisted of leaving a message or cash at a given spot to be picked up by another without making direct contact.

The aim was to arrive at the rendezvous* location spotlessly “dry-cleaned” to drop off or pick up information in complete securitely. The aim was to arrive at the rendezvous location spotlessly “dry-cleaned” to drop off or pick up information securely.

When they were absolutely sure to have gone “black”—" (western intelligence parlance for being undetected—), they would eventually approach the given spot. When they were absolutely sure to have gone “black" (western intelligence parlance for being undetected), they would approach the given spot.

These were highly-trained agents in the surveillance field, which was the responsibility of KGB’s 7th Directorate. These were highly-trained agents in the surveillance field, which was the responsibility of KGB’s 7th Directorate.

These were highly-trained agents in the surveillance field, which wasunder the responsibility of KGB’s 7th Directorate. These were highly-trained agents in the surveillance field, under the responsibility of KGB’s 7th Directorate.

At the end of each test, the students and the surveillance team would compare notes. At the end of each test, the students and the surveillance team would compare notes.

At the end of each test, the students and the surveillance team would compare notes. At the end of each test, the students and the surveillance team would compare notes.

Proverka was nerve-wracking and physically and mentally exhausting. Proverka was nerve-wracking and physically and mentally exhausting.

Proverka was nerve-racking, and both physically and mentally exhausting. Proverka was nerve-racking, and both physically and mentally exhausting.

*is "rendezvous" enough to mean the "meeting" place or is necessary to say "rendezvous' spot"? *is "rendezvous" enough to mean the "meeting" place or is necessary to say "rendezvous' spot"?

I would use "rendezvous spot" (or location, place, etc.).