Q:

What affects air quality indoors after home improvement? 

We installed a new A/C in the corner room of our house a little while back, because we wanted to use it as a nursery.  Installation went fine and the little one sleeps in there every night.  A few months later we decided to get a baby cam, which happens to have an air quality monitor build in.  I noticed strange things happening to the air quality in the room, which reaches concerning levels at times, hence my question:
What affects air quality indoors after home improvement? 
Could the A/C unit itself blow in bad air? 
Could the carpet or the ceiling cause bad air quality? 
Could furniture (mattress / sofa / closet / drawer) cause bad air quality? 
Now, I am obviously aware that keeping the windows closed and consuming air should gradually worsen the air quality, but what has been happening the last nights is more weird than that - the air quality suddenly goes from pretty good to bad in a matter of a few minutes.  Now it could be a problem with the sensor, of course, but I did confirm with a secondary sensor, who gave similar results. 
So, any idea what could cause sudden bursts of pollution into the air? 
Is that an indication of mold or would you expect an A/C to be able to actually worsen the air quality (I generally thought it would improve it)? 

A:

"Air quality" is an ambiguous phrase. 
This baby monitor that you bought, on what basis does it determine the air quality in the room?  Carbon monoxide, carbon dioxide, radon, particulates, pollen, VOCs, smoke? 
There are literally thousands of things that can affect air quality.  I don't think I would get too worried about a baby monitor, that doubles as an air quality sensor, giving you an overall poor reading without knowing why it is showing a poor reading. 
Open the room (and your house) once a week and get fresh air into the room.  If you are really concerned get a better piece of equipment to monitor your air quality that shows specifics about the content of the air.  That would give you a better idea how to remedy poor air quality. 
Good luck!