I looked at the recording surface, thinking I probably wouldn't notice anything. The damage was very obvious: many shiny points on the disk surface. When looked at more carefully, they look like short lines, so they're probably scratches. I was careful when handling the spindle and discs, so this must have happened before they were in my possession. I wonder if the spindle was subject to shock or if this is a defect from the factory.
I made a mistake in assuming that the problems I was having with the first few discs were just due to the visible spots. Even the discs without visible damage are of low quality. There are read speed decreases over large areas of the disc, and PIE/PIF scan results are much worse than with previous good Verbatim discs. After some online research, I found that these the infamous PAP6 discs. My previous good discs were PAPA. That's the start of a code you can see on the transparent area in the middle. Here are two photos comparing PAP6 and PAPA. It's hard to make good photos of this, because it's embossed transparent plastic lettering in transparent plastic. Note how the PAP6 disc has air bubbles in the plastic.
Unfortunately, according to online information, you need to open a package to see if it contains PAP6 or PAPA discs. This means Verbatim media cannot be trusted these days. What trustworthy brands are left? Taiyo Yuden? I used to think that it's weird how some people insist on that brand. Now, it seems they were right. Unfortunately, those cannot be found in local stores. Fortunately, hard drive prices have dropped so much that this is a good time to give up on optical media.