In a recent article in Mises Daily, Benjamin Wiegold argues:
The Drug War Makes Drugs Less Safe
Is his argument right that legalising recreational drugs would improve the quality of supply and reduce the harms they cause?
Decreased quality is a well studied effect of prohibition:
Still another effect of prohibition is increased uncertainty about product quality. Government quality regulation does not exist for illegal commodities, and buyers cannot complain about quality without incriminating themselves.
The Economic Case Against Drug Prohibition
Author(s): Jeffrey A. Miron and Jeffrey Zwiebel
Source: The Journal of Economic Perspectives, Vol. 9, No. 4 (Autumn, 1995), pp. 175-192
Published by: American Economic Association
Stable URL: http://www.jstor.org/stable/2138396
If he is right I can not say, but from what I've read on the topic here are a few points that further argue for the validity of his argument.
It seems to be valid in the limited evidence we've seen in countries where soft-drugs such as cannabis have been decriminalized or legalized. One of these cases which has been considered highly successful is the legalization of cannabis in the Netherlands.
Global drug prohibition’s most glaring weakness and greatest vulnerability is cannabis. As UN experts point out, cannabis is by far the most widely used illegal drug in the world. Cannabis grows wild throughout the world, and is commercially cultivated in remote areas, in backyard gardens, and in technologically sophisticated indoor farms. Just as it was impossible for prohibitionists to prevent alcohol from being produced and used in the US in the 1920s, so too it is now impossible to prevent cannabis from being produced and widely used, especially in democratic countries. As a result of this enormous and unstoppable production and use, global cannabis prohibition faces a growing crisis of legitimacy (Zimmer, 1997). Since the 1980s, the Netherlands has successfully administered its system of regulated, decriminalised cannabis sales. 
Although there are cases such as Portugal and the Czech Republic where hard drugs have been decriminalized as well I am not aware of any papers analyzing the success of these policies.
The text below is a collection of arguments often made in conjunction with the one made in the article linked in the question. It has been added solely for your insight into the argument made.
If drugs were legal, it would open up for public debate. Today people in countries where drugs are illegal people cannot openly discuss quality of suppliers as their identity must remain concealed to prevent their arrest. Another issue is that certain drugs are easier to produce/smuggle with little to no regard for whether that drug is significantly less safe for use, this includes among many other things ecstasy tablets which rarely contain what is advertised (MDMA) exclusively and sometimes not at all. Further is there a common argument from libertarians that regulation is not necessarily needed as legalization would be sufficient for improved competition, especially where market share is controlled with violence and not with quality/price of product.
References for similar reasoning can be found in the answers of both @Articuno and @Ebenezer.
(Thornton 1998) makes this prediction:
Legalizing drugs does not simply reduce the price and increase consumption and addition; instead, it completely transforms these drugs and their markets and results in drug products of lower potency, higher quality, and greater safety for the consumer. The economic model of potency predicts that the re-legalization of drugs would reverse the trends in drug potency, perhaps resulting in significant improvement in the health and safety of consumers.
(MacCoun 2011) predicts a deilemma:
full legalization will probably reduce average harm per use but increase total consumption; the net effect of these two changes is difficult to project.
What actually is the case is something we'll have to wait and see.
MacCoun, Robert J., and Peter Reuter. "Assessing drug prohibition and its alternatives: A guide for agnostics." Annual Review of Law and Social Science 7 (2011): 61-78.
Thornton, Mark. "The potency of illegal drugs." Journal of Drug Issues 28 (1998): 725-740.
Yes, and here is a known case of the war on drugs making illegal use of legal-as-regulated drugs less safe.
In the USA, Legal pain killers can be illegal if abused, i.e. taken by persons not suffering from a genuine medical condition, or taken in excess of the amount directed by the prescribing physician. Pain killer abuse is well known and an issue of government interest: http://www.samhsa.gov/newsroom/advisories/1308215815.aspx
The liver toxic acetaminophen -- more commonly known from the brand name Tylenol -- is a mild pain killer and in the USA, is required to be added to pills containing stronger pain killers. The combined formula is supposed to limit abuse among addicts who seem to be presumed to know that the acetaminophen component could be deadly at the larger dosages in seeking a high from the stronger opioid component of the combined pill. Problem is, who said drug addicts were rational or knowledgeable about this issue?
I remember being annoyed that in order to get effective pain relief I was being forced to take a liver toxin that added little to the pain relieving efficacy of the opiate. I speculated to my wife that there was probably more injury and death occurring from the acetaminophen than the "dangerous narcotic" in the Vicodin.
Now it looks like the FDA has recognized the same thing that was casually obvious to a radiologist more than 10 years ago. As recreational drug users and addicts seek Vicodin for it's narcotic benefits, and regular folks have acute pain, they are increasingly suffering inadvertent liver toxicity from acetaminophen, contributing to the 40,000 Emergency room visits per year related to acute liver injury.
Somewhat earlier in the same article...
Currently some 38% of cases of acute liver failure are due to acetaminophen