The major issues it has, which are apparent even in the beginning, just continue to grow and become harsher to tolerate.
First, the issues with time and pacing. Technology takes time to assemble. When you're building something rather simple and do a jump-cut to a week later when it's finished, that's fine. It's like a baking show that pulls a finished product from under the counter after showing the steps, so we don't have to wait an hour for the oven. But when you start jump-cutting to say, a whole year later? And all of the characters look exactly the same? No changes in relationships, or other progress, etc? It's very jarring. The character in the OP is like the only person to actually visibly change ever. It makes sense for them to, because they were such a little kid, but it just draws attention to the fact no one else does. And jump-cut after jump-cut means there's never any downtime, we just are constantly moving from one plot point to another.
Next is the cast. Dr. Stone has a lot of very interesting and likeable characters. But the author treats them like a team of Pokemon. You can only have so many of them on the active roster at a time, and so the plot has to constantly invent hamfisted reasons for certain people to just disappear in order for the new characters to get a chapter or two to shine, before being tossed back in the box for later.
But the last issue is the most egregious for me. The universe keeps slipping in and out of hentai logic. I;d imagine this is because of the author's former occupation. Dr. Stone tries to be as logical as it can with the science, but that just makes it clash all the harder with things when the hentai rules start to kick in.
What's that? An island of people where women and girls are forcefully taken as tribute to the ugly bastard ruler for his "harem"? Let's infiltrate by dressing up our girls (and a guy) as bait, and just kind of laugh off the fact that the enemies are trying to rape them. This is about where I dropped it, but from what I've seen, the trend continues on past that.
Basically, the beginning of the manga was really interesting and made up for its flaws, but once Tsukasa is no longer the main antagonist, it just snowballs out of control, and the problems grow until you can't ignore them anymore. The way people are turned to stone is revealed way too early, for no reason, and is underwhelming to say the least. The enemies are uninspired and not very compelling. The science becomes less and less believable, as well as the time it takes to make it. You get less time with the members of the cast you actually like. So on and so on.