Obviously, the risk of airborne transmission of disease increases based on proximity, but are airplane cabins particularly more unhealthy than, say, train cabins? Is there something (e.g., air recirculation) that justifies greater than normal caution? Anyone who's been to an airport convenience store knows that there are several products that play up this belief, but I'm not asking about the merits of such products, only the underlying premise.
This review "Medical issues associated with commercial flights" from The Lancet in 2009 covers most of the points.
The most substantial issue seems to be cabin pressure, causing fatigue, headache, lightheadedness, and nausea, and other more serious problems for those with certain medical conditions. The review then goes through other issues such as venous thromboembolism risk, cosmic radiation, jet lag, and infectious diseases. My impression is that these may be in the authors' view of the order of significance.
On air recirculation, there was a 2002 study not suggesting there is extra risk, though there have been many cases of infection traced to aircraft; there clearly is the general issue that in an aircraft you are more likely to be sitting next to somebody with an exotic foreign disease than if you are in your own car.
The recirculated air is often given as an example, but according to http://www.boeing.com/boeing/commercial/cabinair/facts.page#4 "The efficiency of HEPA filters to remove bacteria and viruses (.01 to .1 microns) is greater than 99 percent." so the air in an aircraft is probably cleaner than most other air.
At http://www.nbcnews.com/id/34708785/ns/travel-travel_tips/t/airplane-air-not-bad-you-think/#.VEkB0sm0Qbw it says "On average, cabin air is completely refreshed 20 times per hour, compared with just 12 times per hour in an office building. On most aircraft, air is also circulated through hospital-grade HEPA filters".