A recent [AskScience thread] (https://www.reddit.com/r/askscience/comments/4x84e4/discussion_veritasiums_newest_youtube_video_on/) focused on the lack of resources for reproducing experiments as a way to verify the results.
The parallel for history seems to be the frequency of spending time and money tracking down sources - especially if they are obscure, physical materials - and reading through them to find the relevant information. Are the resources spent on this unacceptably low?
Related questions:
I check sources for papers in my own "backyard," so to speak. Which is to say:
if I'm doing research on the same topic (more or less)
if I think the source matters for their or my argument
if I think there's any chance at all it doesn't say what the other historian claims it does, or that the historian's interpretation could be wrong or incomplete
and I can get the source one way or another (and understand it — e.g., it is in a language I read)
...then I'm checking it. Which is to say, I'm getting my own copy.
Sometimes the last part (access, both physical and linguistic) is, of course, a big barrier, and if I'm going to get something really obscure I've got to have a real reason. But with online sources, digitization, and databases, this is getting easier all the time.
But if the question is, do historians do this systematically?, the answer is basically "no" and there are no resources "spent" on this except the same ones we use for our own research. Which is a difference between us and the sciences: it's much easier to check a source, even in an obscure archive, than it is to re-run most science experiments. If you have a precise citation for something you can usually just order a quick photocopy (I do a lot of "order out" archive diving recently — it's cheaper to pay $100 for an archive to photocopy the couple of folders I care about than it is to actually go there).
I don't think history has a "reproducibility" problem because that's not our game (we are not doing experiments). There have occasionally be forged, faked, and just made-up sources. Occasionally these have been high-profile, to be sure, but for anything that any other historian cares about, the other historians will eventually visit the same archive, look at the same sources, and so on. Not so much because they suspect other people of fraud, but because unless you've got the thing in front of you, you are still reliant on someone else's eyes and brains to make sense of it and its documentary context. I don't know about other historians, but I'm not a big fan of that, so if I'm going to go out on a limb for anything, I'm going to try and track it down. In any case, outright fraud is different than the kind of problem posed by lack of reproducibility.
Many things in history are subjective, but much isn't. We can argue all day about what a source means, but it's much easier to agree when someone has misquoted a source, or cited a source in support of something that the source doesn't describe. It's also easy to spot misidentified artefacts and texts, or disproven ideas about sources' meanings. My answer below is talking about these kinds of errors: things that most good historians would look at in peer review and say, 'No - that is not what you say it is.'
To answer your questions:
Somewhere in between. There's simply not enough time to check every footnote, and I have to take a lot on faith.
No. Peer review for academic journals is voluntary (unpaid), and has to be done in free time. It can be time consuming (I spent a full day and a half checking the figures and statistics on a paper I reviewed recently - I'm glad I did, as I found numerous errors, ie the system worked). In research more generally, as well, support is limited. There's intense pressure to produce work quickly, both as a graduate student and to get tenure. You're expected to know your own primary sources back to front, but it's rare that you're given support to check others' work. One does what one can, but few scholars manage to do as much as we need to.
Yes. I know a few historians who really read all the primary sources in their field. I know dozens more who know their own sources, but accept what others write. I strike a balance, personally, as I think most of us do, between critically questioning and assuming that my colleagues are competent.
The results are mixed. When I have taken the time to dig into my sources - really dig - I find problems. Sometimes authors play telephone, where one person cites a claim that another cites and another, and when you read the original it's far less definitive than the statements it morphed into through repetition. More often, one author's interpretation gets accepted as fact and the original sources are just read through that lens repeatedly by other scholars who don't have the time or inclination to check the original text. Sometimes there are factual errors and misreadings that no one bothers to correct. (The classic example here is the story that Rome salted the fields outside Carthage after the Punic War. You'll find this story in hundreds of books, but no original sources. It was invented in the 19th century, and repeated so many times that, years after having been debunked, it's still repeated.)
More recently, there have been some really cool big data studies in early medieval archaeology. They're great because they tie together multiple datasets and use statistical analyses to get a lot of cool patterns from them (especially when it comes to mapping social trends through time and space). But they're only as good as the quality of the data they use. My dissertation research gave me the chance to check one of these datasets, and I found it to be grossly inaccurate, to the point where I'm not sure whether it can be salvaged as more than a bibliography. Yet I have met multiple PhD students - and full faculty - who are working with pre-existing datasets and not re-examining them for errors, because they don't feel they have the time to second guess them. One PhD student said, in justification of this, 'I trust ___ to have been a professional.' Yes, ok - but if you aren't going to check the data, who will? This is how errors are perpetuated in the sciences, and historical disciplines aren't immune.
It's endemic, and it won't change until we as a discipline reduce publication expectations and emphasize publication quality over publication volume.
My PhD thesis builds upon and expands an earlier treatment of a specific topic and as a result, I did go through almost all the source material (all that I could locate, that is). In addition, I've added more sources and contrast the developments described in the original work to developments elsewhere.
These inspired me to do a retelling of the story with conclusions that are somewhat different from the original. The original thesis is not "wrong" but, I argue, somewhat incomplete and at times perhaps unintentionally misleading even.
Emboldened by these findings, I've also looked at primary sources for two more case studies that have been important in my (admittedly very narrow) field and found some inconsistencies there as well - I'm writing (or I should be writing) a paper about these right now.
But a rule of thumb that should be remembered is that if you dig deep enough, you can always find "evidence" to overturn or at least question any case study.