Disease was actually not a huge problem compared to the threat of hostile natives and wild animals. However, while traveling, the men would often drink from the rivers which caused them to suffer from terrible boils on their skin. This may have been an infection caused by the Staphylococcus bacteria. Don't quote me on that though. There was also a shortage of fruit and vegetables, but whether this caused any vitamin deficiencies I do not know. It it true that the men suffered from a venereal disease believed to be syphilis which they contracted from sleeping with native women at Fort Mandan. White traders had previously brought syphilis to the Mandan population and the treatment of the day was a mecurial ointment - which is, of course, no cure; it only allays the symptoms. There is no evidence that either Lewis or Clark ever had an intimate relationship with these women as they were not only government officials and therefore had to set an example, but they were also very busy as leaders of the expedition.
As for Lewis and Clark particularly, they did not suffer from disease except for the one time that Lewis had a bad case of the flu one winter. They did have injuries though, as Clark suffered from a "rheumatism of the neck" and Lewis was accidentally shot in the left thigh while hunting.