What would be wrong with someone to have blood in their saliva?

Depends. Most commonly this is from gingivitis/periodontitis/gum disease...See your dentist for eval and thorough cleaning. Less common, bleeding ulcer/discharge from sinus/ulcerations in mouth or throat.
Gingivitis. Actually you could have a number of different issues but gingivitis is the most common reason to have blood in saliva. Advanced periodontal disease can also cause blood in saliva. I would get checked by a dentist to rule out any of the above and if you're oral health checks out fine then go to your regular md for an evaluation.