There is actually a ton of replication going on at any given moment, usually because we work off of each other's work, whether those others are internal or external. But, reporting anything basically destroys your career in the same way saying something about Weinstein before everyone's doing it does. So, most of us just default to having a mental list of people and circles we avoid as sketchy and deal with it the way women deal with creepy dudes in music scenes, and sometimes pay the troll toll. IMO, this is actually one of the reasons for recent increases in silo-ing, not just stuff being way more complicated recently; if you switch fields, you have to learn this stuff and pay your troll tolls all over again. Anyway, I have discovered or witnessed serious replication problems four times --
(1) An experiment I was setting up using the same method both on a protein previously analyzed by the lab as a control and some new ones yielded consistently "wonky" results (read: need different method, as additional interactions are implied that make standard method inappropriate) in both. I wasn't even in graduate school yet and was assumed to simply be doing shoddy work, after all, the previous work was done by a graduate student who is now faculty at Harvard, so clearly someone better trained and more capable. Well, I finally went through all of his poorly marked lab notebooks and got all of his raw data... his data had the same "wonkiness," as mine, he just presumably wanted to stick to that method and "fixed" it with extreme cherry-picking and selective reporting. Did the PI whose lab I was in publish a retraction or correction? No, it would be too embarrassing to everyone involved, so the bad numbers and data live on.
(2) A model or, let's say "computational method," was calibrated on a relatively small, incomplete, and partially hypothetical data-set maybe 15 years ago, but, well, that was what people had. There are many other models that do a similar task, by the way, no reason to use this one... except this one was produced by the lab I was in at the time. I was told to use the results of this one into something I was working on and instead, when reevaluating it on the much larger data-set we have now, found it worked no better than chance. Any correction or mention of this outside the lab? No, and even in the lab, the PI reacted extremely poorly and I was forced to run numerous additional experiments which all showed the same thing, that there was basically no context this model was useful. I found a different method worked better and subsequently, had my former advisor "forget" (for the second time) to write and submit his portion of a fellowship he previously told me to apply to. This model is still tweaked in still useless ways and trotted out in front of the national body that funds a "core" grant that the PI basically uses as a slush fund, as sign of the "core's" "computational abilities." One of the many reasons I ended up switching labs. PI is a NAS member, by the way, and also auto-rejects certain PIs from papers and grants because "he just doesn't like their research" (i.e. they pissed him off in some arbitrary way), also flew out a member of the Swedish RAS and helped them get an American appointment seemingly in exchange for winning a sub-Nobel prize for research... they basically had nothing to do with, also used to basically use various members as free labor on super random stuff to faculty who approved his grants, so you know the type.
(3) Well, here's a fun one with real stakes. Amyloid-β oligomers, field already rife with fraud. A lab that supposedly has real ones kept "purifying" them for the lab involved in 2, only for the vial to come basically destroyed. This happened multiple times, leading them to blame the lab, then shipping. Okay, whatever. They send raw material, tell people to follow a protocol carefully to make new ones. Various different people try, including people who are very, very careful with such methods and can make everything else. Nobody can make them. The answer is "well, you guys must suck at making them." Can anyone else get the protocol right? Well, not really... But, admittedly, someone did once get a different but similar protocol to work only under the influence of a strong magnetic field, so maybe there's something weird going on in their building that they actually don't know about and maybe they're being truthful. But, alternatively, they're coincidentally the only lab in the world that can make super special sauce, and everybody else is just a shitty scientist. Does anyone really dig around? No, why would a PI doing what the PI does in 2 want to make an unnecessary enemy of someone just as powerful and potentially shitty? Predators don't like fighting.
(4) Another one that someone just couldn't replicate at all, poured four years into it, origin was a big lab. Same vibe as third case, "you guys must just suck at doing this," then "well, I can't get in contact with the graduate student who wrote the paper, they're now in consulting, and I can't find their data either." No retraction or public comment, too big of a name to complain about except maybe on PubPeer. Wasted an entire R21.