From a current Medical Student as taught by Medical School Professors.
You Should not mix Acetaminophen (Tylenol)
and Acetylsalicylic acid (Aspirin).
The reason for this is long term renal (kidney)
What happens in the Tylenol induces the formation of free oxide radicals which damage tissues (especially the kidneys and liver).
This is normally not an issue at low Tylenol doses.
when you add Aspirin to the mix,
the free oxide radicals become an issue.
Aspirin is a Cyclooxygenase inhibitor (COX),
which decreases prostaglandin (PGE 2)
Prostaglandins are responsible for vasodilatation of the renal afferent arterioles.
If you are on Aspirin the renal afferent arterioles are vasoconstricted and subsequently renal blood flow is decreased.
When renal blood flow is compromised your kidney is less able to deal with the free oxide radicals produced by Tylenol.
So what happens?
The free oxide radicals damage the renal medulla (which may slough off)
or lose the ability to concentrate urine due to damage to the most notably the thick ascending limb of the nephron.
This is called Analgesic Nephropathy.
Having said this,
the damage is caused by long term mixing of Tylenol and Aspirin,
so having mixed the two in the past once five years ago is not going to compromise your kidneys.
Just make sure to avoid the mistake in the future,
and Pass on this information (there are way too many sources providing incorrect information on this subject).