One serious problem with panic attacks is that they are often mistaken for other afflictions, such as asthma attacks or heart attacks. The result can be (and often is) that the panic attack is misdiagnosed and treated inappropriately.
As an asthma sufferer myself, I have witnessed people in the throes of a panic attack - and mistaken them for fellow asthmatics. The error is very easy to make, since the surface symptoms (wheezing, difficulty breathing, clammy skin, physical weakness) are very similar.
Furthermore, though patients with a predilection towards panic attacks are undoubtedly suffering from a genuine and very debilitating ailment, there is a tendency to disregard their behaviour as mere hysterics. In particular, it is a deplorable fact that gender bias is often applied (both by health care professionals and by friends and relations) - female patients are often regarded as hysterical hypochondriacs, and male patients are often treated with condescension, as cowards.