Do mutt dogs have hereditary health problems?

[JFRICK]

Hey all, my sister and I adopted 4 mutts about 10 years ago when they were puppies that we found on the side of the road. Anyway, I'll give a brief description of them b/c I think they may have had different fathers..

Eddie (male) short, thick, course black hair with the markings of a Rotty.
BH (male) short, thin, soft hair. Has a black spot on his tongue.
Molly (female) (no longer with us) had short, thin, course, kind of rusy colored hair.
Elgie (female) (my sister adopted her) Long, thick, black hair, also has a black spot on her tongue.

Would you think they have different father b/c of the differences in all of them, although they are all about the same size, in the 50 pound range?

My main question is this....Do mutts in the same litter usually have the same health problems, as in hereditary problems? Molly developed cancer about 2 years ago on her spleen, had that tumor removed, but about 6 months later had to put her down b/c the cancer had spread to her brain. She was 8.

Now that the other's are 10, I'm curious as to if I should be watching for cancer in them? Eddie recently developed a cyst of some sort on his back leg around the knee joint. The lump is kinda spongy feeling, it rolls around under the skin, and it doesn't seem to be causing him any pain. I'm thinking it's just a fatty cyst, but I'm taking him to the vet tomorrow to get it checked out.