Drywall – Ceiling drywall separating from trim sign of bigger issues or bad installation

I'm not 100% clear as to whether you bought the house with the cracks and the popped out nails, or whether it has happened since you bought the place. If it has happened since you bought the place then I would be concerned and have it looked into. If it was like that when you bought it the damage could have been there for decades, there's no way to know for sure unless you can speak to the former owner.

I'm assuming you've done this or you have a slab foundation, but if you have access to the foundation like a crawlspace or a basement have a look to see if there's any evidence of settling. Try and mark off the cracks and the positions of the nails in ways you can later go back and check for movement. Use a ruler to draw a pencil line perpendicular to the cracks every inch or so, and use a grease pencil for the nails, or a permanent marker. Keep an eye on them every few weeks and see what happens.

I've encountered the same problem in my own home, although the drywall and ceiling seam cracks only showed up one at a time over the course of a few years, and most of them were present when I moved in. If more than one or two seams popped or nail heads started showing within a month, that seems like it could be a rather large settlement in your foundation, or some other structural problem.

I'd highly recommend getting a foundation specialist to your house sooner rather than later to see if your foundation might need piers to support part of it, or if some other repair is required. In my house, a total of 14 piers were needed along the side and front of the house to support one side and prevent further shifting. There were a few hairline cracks (even small cracks can be a bad sign depending on where and how many they are) in the foundation walls, and the corner of the house had settled over 2" before the problem was found.

The problem could also be in load-bearing structures (walls, I-beams in the basement, etc.), especially if it seems the problems are mostly towards the middle of the house.

The sooner you get this fixed (don't just let it go, even if you have to pay a few thousand), the better. You'll avoid more drywall repair later, and prevent further settlement and degradation of your house's structural integrity.