Right, but also with a sort of labor-saving aspect to it. Everything needs to be checked by somebody. Not everything needs to be checked by everybody.
For an extreme example, there are lots of derivations in Jackson's electrodynamics textbook which I have not checked for myself. I am very, very confident that I can use the results without checking and not come to regret it later. Jackson is a reliable person individually, plus I know the heritage of the textbook and the number of people who know its details inside out. The LIGO collaboration, sure, they wrote a paper and I am sure (from personal knowledge) that every sentence in it was read and agreed on by dozens or hundreds of people. (Which is not to say nobody made a mistake, but certainly that nobody made a glaring mistake.) When I'm reading a brand-new, small-audience, small-author-list paper? Yes, I'm on the lookout for errors, especially when the authors are outside their expertise (the data-analysis section of an instrument-builder's paper is sometimes dodgy, for example; or the places where a theorists' paper tries to sketch an experimental apparatus.) Everything should get checked by someone---sometimes by me.
Yep.
And there are some sometimes quite subtle aspects to this, as I know from my own, entirely independent, research.
For example, in arXiv you often read a Comment (in the abstract page) like "Accepted for publication in (journal)", which leads you to think that the arXiv version is essentially the same as what you'll get if you penetrate the journal's paywall (there will be formatting differences, some grammar/spelling changes, etc). And I'm sure that in most cases this is so. HOWEVER it is not always!

For example, mistakes happen, and the lead author posts a v1 draft instead of what was actually submitted (and accepted).
Then there's laxity due to extreme familiarity. For example, I've come across figures with ridiculously wrong axis labels, even in highly cited papers (e.g. should be log(sols), but is labelled sols) ... pros in the narrow field don't even see the error.
And wasn't it found, when machine checking became available, that a ridiculously high number of printed solutions were wrong (a book of integrals? I don't remember; many years ago now)?
Here's a bugbear of mine: "in press" or similar ... a citation/reference in a paper to one that has not yet been published. Sure, many such do, in fact, get published, often quite soon afterwards. HOWEVER I have come across rather too many which, it seems, were never published.
Then there's "the data this paper totally depends upon are available at this URL" (paraphrase, OK?). Really? I've found some real whoppers ... broken/bad links, totally different datasets, gibberish, ... Contact the lead author to get the real scoop? After all, their email addy is in the paper! Well, that often doesn't work either ... why would a scientist respond to a mere Jean Tate of no "institution"? and the email addy is dead, the author now works somewhere else, ...
I read one arXiv abstract which had the comment "Accepted for publication in (journal)" ... it was over two years' old, and no such paper had apparently been published, in (journal), or any other.
So, yeah, Jackson is surely reliable; for the rest?