Biochemist Ray Peat has been pointing this out for years now.  There
was a recent report of an experiment done (you can go to
sciencedaily.com and search for fried polyunsaturated and it should be
the first item) on a product of linoleic acid called 4-HNE.  The
interesting thing is that I found a scientific paper that noted that
another product of linoleic acid was much more damaging than 4-HNE,
which is very bad stuff indeed.  You can go to pubmed.com and search
for some key words, such as lipid peroxidation, and you'll see that
this is the worst thing you can eat, yet it is being promoted as
"essential."  Do a search of pubmed.com for spiteller lipid
peroxidation and you'll see several reports by a group of scientists
that have specialized in this direction.  There are scientists who
state in their abstracts that lipid peroxidation is the underlying
cause of all "chronic disease," and from my extensive research over the
last 4 years, I'd have to agree.  Free iron is a problem, but as
Spiteller mentions, when cells are damaged, a cascade of events
results, iron gets liberated along with linoleic acid (or the fatty
acid derived from  linoleic, called arachidonic), and several very
dangerous molecules are formed, which then can do severe damage to
cells and organs.  Because there is no real scientific evidence to
suggest that a full grown adult needs linoleic acid (and plenty to
suggest it is nothing but harmful), I restrict my intake of it to trace
amounts.  When  you do that, your body makes its own polyunsaturated
fatty acid, called the Mead acid, which is much more stable and does
not form such harmful substances.  There are several studies showing
that people or animals with Mead acid instead of omega 6
polyunsaturates in their tissues have lower inflammation or are more
resistant to it, which makes sense biochemically.

If you do a search for arachidonic depression on sciencedaily.com
you'll see that the levels of this horribly damaging substance are
elevated in depressed patients brains, and there is something called
arachidonic cascade mania, another biochemical situation that leads to
psychological disorders.  Indeed, the so-called epidemic of autism is
likely due to the much higher intake of linoleic acid now, as compared
to 30 or so years ago.  It wouldn't take much to test this idea, and
pleny of scientists are writing about it, but the big healthy agencies
are usually looking for bacteria, viruses, high cholesterol, or
something else that is either irrelevant or a secondary phenomenon.

Although montygram's views on PUFAs are extreme, I personally back
his statement that omega-6 PUFAs are undesirable in a human diet.

Omega-3 PUFAs are a totally different matter. Whether they can be
found to be carcinogenic or not, whether they peroxidize or not, is
irrelevant. They are essential to the operation of human brains.

For me the question is: how much omega-3 do we need as adults to
maintain our brains? I haven't yet seen a quantitative study of that
question that I trust. Until then, I shall make sure I consume a
significant quantity of them.
(cf. http://sankey.ws/dietref.html)

"Polyunsaturated lipids are an acceptable substitute when
monounsaturated lipids are not readily available"

Gee, it's nice that pure olive oil tastes so good  :-)
(There are super Italian and Greek communities in Ottawa.)

"Especially DHA seems to be important."

True. But always keep in mind that the deterioration rate of our various brain
components may vary, perhaps greatly. The required replacement rate,
times the efficiency of transfer of dietary component to our brain,
is what will determine the correct dietary response.