There have been a few records of Otterhounds with bleeding disorders. The Otterhound Club of America is in the process of completing a health survey of the breed in the US and preliminary information indicates major health problems are uncommon. This breed is usually quite slow to mature, both physically and mentally. Though some Otterhounds do have a fair amount of coat they do not shed a great deal. Expect to brush an OH on a weekly basis to keep the coat from matting.
Otterhounds have big hairy feet that are attracted to mud.
Most OHs aren't slobbery dogs, but they've got beards and long hairy ears that get into their water bowls, food dishes, etc., and then act as transport mechanisms to spread water, food, etc. around. Unless you are actively showing the dog, frequent baths should not be necessary. You will probably need to clean ears on a regular basis. Otterhounds have a deep bay, a lovely melodious sound, which carries amazingly well. Some OHs are fairly quiet, and some seem to like the sound of their own voice.