The core appeal of the show is very formulaic and easy to grasp. This genius character who has been isekaid into a stone-age setting will spend an episode recreating modern conveniences with extremely basic tools. Fires, pulley systems, medicine, that kind of thing. It's treated like a semi-educational segment, with pop-ups on-screen and intermissions that encourage the viewer to try crafting some of this stuff on their own (except the bomb, which has a warning that the instructions, while accurate, are dangerous).
The take-away from this is that after an episode you'll find yourself walking around your home drinking/eating something or using some tool, and you'll stop and appreciate how cool it is that humanity has come far enough for you to have [cool thing]. The philosophy of the show is all about building humans up and appreciating every inch of progress we make, and it really puts you in a good mood. When Dr. Stone is doing this, it's extremely fun. The plot takes a backseat to the core theme of human progress, and storytelling is usually secondary to showing off cool and revolutionary inventions.
The downside comes in midway through the first season, though I won't spoil plot details. The protagonist, an egomaniacal genius, begins getting ego-stroke moments that are very standard isekai fair. Female characters all are pointlessly sexualized in uncomfortable ways, and the power fantasy starts to build up a childish scenario onto which the horny, power-hungry viewer can project themselves. This is particularly frustrating for this show because it means I can't recommend it for kids, even though it would otherwise be a stellar pick.
The shonen elements creep into Dr Stone more the longer it runs on, pushing characters into scenarios they have to fight their way out of rather than just taking their time step-by-step making technology. One arc, in particular, is very stock shonen (you'll know it when it starts) and I would recommend just skipping it entirely because shonen simply isn't what the show does well. There's a fan-edit to be made that could definitely solve these problems one day. I can at least say that it gets mostly back on track, and you certainly won't be left with a bad taste in your mouth by the finale.
