Science is a self-correcting system. In the context of scientific publishing, this means to me that a certain amount of research is presented in a paper, after which potentially contradictory follow-up papers are published and may ultimately lead to a paradigm shift in the field.
Retractions are a whole different thing. They occur when the author, or worse yet, the editor, deem an article unworthy of remaining within the scientific literature. In its retraction guideline, the committee on publication ethics (COPE) defines reasons for an editor to retract a paper: the editor has clear evidence that the findings are unreliable, either as a result of misconduct (e.g. data fabrication) or honest error (e.g. miscalculation or experimental error); the findings have previously been published elsewhere without proper cross-reference, permission or justification (i.e. cases of redundant publication); the publication constitutes plagiarism; the publication reports unethical research.
The international committee of medical journal editors (ICMJE) calls for authors to retract their own problematic papers, and for editors to sign the retractions only if the authors are unwilling or unable and “other responsible persons” (i.e. representatives of the authors’ institution) do not volunteer to sign the retraction notice.
Recent studies have shown that the rate of retractions has increased in recent years[1,2], a trend that can be viewed as a good thing, in that the system is working and discarding problematic works, or it can be viewed as a worrying manifestation of the declining standards of scientific research.
What happens when an article is retracted? Rather than just being removed from the journal and all of its archived forms, an official retraction notice has to be issued. COPE’s guideline includes suggestions for the retraction notice: It should be linked to the retracted article wherever possible; clearly identify the retracted article; be clearly identified as a retraction (i.e. distinct from other types of correction or comment); be published promptly to minimize harmful effects from misleading publications; be freely available to all readers; state who is retracting the article and the reason(s) for retraction. Adhering to these guidelines leads to a situation in which the citation remains in the literature, either with the title and authors’ names, or just with a digital object identifier (DOI) and marked as retracted (One example).
The implementation of these recommended transparency measures is incomplete, and in addition, many of the retracted papers remain on personal websites and online repositories without any identification as retracted. As a result, retracted papers keep getting cited.
A prominent force in disseminating the information about retracted papers is the blog retraction watch.
Started in 2010, it tracks retractions and presents them by location, author and journal as well as other classifications. The authors write the stories behind retraction notices and issues pertaining to research misconduct. Many of their posts are fascinating (if sometimes worrying) reads and I recommend checking their website periodically.
It is of course unreasonable to expect authors to double-check every paper they cite to make sure it has not been retracted. However, if a large proportion of one's research is based on a specific publication, it is good practice to occasionally make sure that specific publication has not been retracted or substantially refuted by other publications.
 da Silva JAT, Bornemann-Cimenti H. Why do some retracted papers continue to be cited? Scientometrics. 2017;110(1):365–370.
 Madlock-Brown CR, Eichmann D. The (lack of) impact of retraction on citation networks. Sci Eng Ethics. 2015;21(1):127-137. doi:10.1007/s11948-014-9532-1.
 Moylan EC, Kowalczuk MK. Why articles are retracted: a retrospective cross-sectional study of retraction notices at BioMed Central. BMJ Open. 2016;6(11):e012047. doi:10.1136/bmjopen-2016-012047.