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Ahem, you could say that: like there were some civil rights problems in Saddam's Iraq. .DOC files can carry macros, which are powerful enough to run your system through a leaf chipper in front of its network peers. You can download the file without invoking them, but not examine it -- which means basically the virus vectors are perfectly and completely secure against the computer owner. There are people who think that is what computer security ought to mean: Microsoft, the MPAA, virus writers.
There are "some portability problems with .doc files" also: you have to hope your audience has the same version of Msword that you do.
PDF files are highly portable, and "more secure than viewing ANYTHING with the Infernal Explorer" (although IIRC, there was once a potential minor security problem with them also.) Compared to Flash, they share the advantages of vector graphics, but have better portability, infinitely better security, and are cheaper to produce. They also have the enormous advantage of NOT tempting stupid graphics artists into gratuitous animations.
They share with Flash the disadvantage of tempting thoughtless content developers into very large files. You can do the same stupid thing with HTML, so I'm not sure why it's so much bigger a temptation with PDF.
Recommendation: PDF is the only way to fly when you need to control exactly how a page looks. But when you post a link to a PDF file, always include its size, so surfers will know YOU'RE NOT one of those thoughtless Great-American-Novel-In-One-File kind of publishers.