We always hear about scurvy with regards to sailors but there doesn't seem to be much common knowledge on other potential health issues that sailors experienced.
For example, was skin cancer a major problem back then? Or was the life expectancy low enough that it was more common to die or have problems from other things before skin cancer was able to develop far enough to be problematic?
I asked a friend of mine (see his website here who now joined because of the response to his post here as /u/RMission) who researches seventeenth and eighteenth century maritime medicine, and with specifics towards skin cancer, provided this answer:
My answer would be something along the lines of "Almost certainly, but they didn't know it and medicine would rarely have recognized it as such." I don't really collect info in my notes on anything relating to the term cancer because the meaning differs between texts and sometimes even individual disease discussions within the same text. However, they would have had skin cancers then just as we do now.
From sea surgeon John Moyle's book, "Cancers are usually extirpated [rooted out and destroyed], and the place brought to digestion [filled with healthy skin] and healed. You can extirpate a Cancer with your Catling [knife], but if a Finger or Toe, you extirpate it with your Chizel and Mallet." (Abstractum chirurgiae marinae, p. 87)
Enticing, but not really enough to answer the question. See, bubos [growths resulting from syphilis] were also thought to be cancers. Plus Moyle lumped cancers in with ulcers, tumors and fistulas. So what are we dealing with here? It COULD be skin cancer. It almost SOUNDS like it is, but is it?
As for learning about other health issues at sea, there are works you can look into concerning the subject: Brown, Kevin. Poxed and Scurvied: The Story of Sickness and Health at Sea. Annapolis, Md: Naval Institute Press, 2011.
Thank you all for the insightful and detailed answers! Very interesting stuff.