Is there any tool to make checking that referencing is correct easier?
I sometimes find that after I've written a lot of text I begin to question, whether it is possible that I've referenced wrong pages somewhere or mistyped a source or something.
Better BibTeX for Zotero also can identify similar issues when you export to a bibliography file. These are written as comments in the bib file.
Both these options tend to identify issues that I don't think are actual problems, unfortunately. But they can be useful to spot some real problems. I vaguely recall once finding out that I typed in an ISBN wrong from biber, for example, as ISBNs have check digits.
I've also used a small script I wrote myself to catch some errors. For example, in Zotero if I don't know the end page of an article before I get it, I'll put eoa (short for "end of article") in as the last page. I might forget to update Zotero after I get a copy of the article. This script will identify all instances of eoa in the pages field of my bib file so I can put in the real end page. I also have some consistency checks like identifying instances of "Ph.D." so I can change them to "PhD".
These options won't determine that you have the wrong pages or anything like that. In principle, you could determine if a page range is impossible (for example, pages 115-101 is likely a typo). You might want to write your own script to catch that, though I wouldn't expect that particular problem to be common.
It also is possible to automate getting citation information from a DOI and check consistency with that. But if you use Zotero or another reference manager, this will not likely change much.
This may be more useful for most people to make sure that their bibliographies are correct: I would recommend avoiding getting citations from less-reliable sources. For example, many times now I've found that Google Scholar has the wrong or incomplete citation information. In contrast, Zotero on journal websites has worked very well in my experience. Only rarely do I need to correct the citation data.