From the paper,

> We obtained de-identified whole blood samples from 14 astronauts who flew relatively short Space Shuttle missions (median 12 days) between 1998–2001. These samples were stored at −80°C for ~20 years. Blood samples were collected 10 days before flight, the day of landing, and 3 days after landing12. However, for this specific study, only samples from 3 days after landing (R + 3) were collected as buffy coats (peripheral blood mononuclear cells - PBMCs).

One of the issues here is of the biased sample set. To say that astronauts are drawn from a small pool is a severe understatement. All astronauts from the stated era have,

    - High IQs
    - Absence of obvious psychopathologies
    - Extremely high stress tolerance
    - Faster (than the median) reaction times well into middle age
    - Usually within 3SD for M/F height, falling between 5' to 6'2 (6'4 at most)
    - High educational attainment

And they've all done,

    - Scuba diving (sometimes including extended stays as aquanauts)
    - Pilot training (even if you're a scientist astronaut, they'll teach you how to fly, [edit - as Walter points out flight hours equal radiation exposure and NASA astronauts usually have to maintain a minimum of 180 hours per year to retain their flight status])
    - *At least* one sport where they've risked their life
    - Undergone wilderness survival training, including a "hell week" of some sort, somewhere along the line
    - Experienced near drowning (part of training) and other similar stressors
    - (frequently but not always) Been a part of the military, including exposure to pollutants that we now know are carcinogenic or harmful.

Additionally, during this period, unless they were an international astronaut,

    - They would eat similar foods, from the same places
    - Live in close proximity to each other
    - Grow up in roughly similar environments (though split between urban/rural environments)

Of course, not all of these factors will impact their DNA, but the selection and similar life experiences creates a unique problem. Until we send more people up, we won't have enough data to say how space travel impacts and mutates us.