In the movie Alien the character Kane becomes an unwitting host to an alien parasite, which eventually kills him. Why was this parasite not detected after the face-hugger died and fell off? Was the Nostromo without any medical imaging systems? Or did they just not think to run any kind of scans on him after he was released?
Who says they didn't? Remember that the scanner was being run by Ash (who was Science Officer) who had something of a hidden agenda, even if he did detect it he wouldn't have said anything...
Ash knew about the embryo in Kane. He is studying it from a scan but when Ripley comes over he turns the screen off.
Ripley: It's amazing. What is it?
Ash: Why yes it is, um... I don't know yet.
You have to remember Ash is a synthetic and on the ship specifically to observe and under orders to get the lifeform back to Earth even if it means killing the whole crew who are expendable to the company.
"Bring back lifeform. Priority one. All other priorities rescinded."
Since an Alien can grow from chest-burster to full-grown 7' tall adult in around 8 hours, when the initial egg was planted, it might have been very tiny, and might have been too hard to see on a general scan. And since the Alien is not made of bone, it's egg might consist of semi-transparent papery material that doesn't image well.
But more likely it was that Ash was hiding it.
In the final version of the shooting script (the one on which the film's novelisation was based) we see precisely why the alien wasn't detected in Kane's abdomen after the facehugger removed itself; because Ash didn't put Kane back through the Autodoc's X-Ray scanner, relying purely on blood, fluid and temperature tests to inform them about his condition.
You may wish to note that although Ripley had observed the eggs on the scanner, Ash wasn't able to get a good view of them (surprise, surprise) and had advised the captain that the "shadow" on Kane's lungs was likely caused by a malfunctioning X-Ray scanner head rather than a real object.
This supposed malfunction would easily explain his reluctance to use the scanner again should anyone ask, which they apparently didn't.
RIPLEY: What about Kane?
Ash turns back to the bunk. Studies the life support gauges. Kane continues to breathe steadily.
ASH: Running a fever. And still unconscious. The machine will bring his temperature down. His vital functions are strong... who knows, he may make it.
To get Ripley's mind off Ash and vice versa, he turned the conversation back to Kane. 'Unconscious and a slight fever. Anything else?'
Ash studied readouts. 'Nothing that shows here. His vital signs continue strong.'
Now since covenant came out we know ash knew the whole time. The Nostromo was bunk from the beginning with false pretenses. I believe he is looking at a slide of a "shock trooper" as David describes when going through his various creations.