Single gene defect causing multiple unrelated problems is termed as the following:

Pleiotropy refers to the phenomenon whereby a single mutant allele can have widespread effects or expression in different tissues or organ systems. In other words, an allele may produce more than one effect on the phenotype. For example, Marfan syndrome has manifestations in different organ systems (skeletal, cardiac, ophthalmologic, etc) due to a single mutation within the fibrillin gene. Penetrance refers to the propoion of individuals with a paicular genotype that express the same phenotype. Pseudodominance is the term given to an apparent dominant inheritance pattern due to recessive defects in a disease gene. Anticipation is used to describe an unusual pattern of inheritance in which symptoms became manifest at earlier ages and with increasing severity as traits are passed to subsequent generations Ref: Tsaic A.C., Manchester D.K., Elias E.R. (2012). Chapter 37. Genetics & Dysmorphology. In W.W. Hay, Jr., M.J. Levin, R.R. Deterding, J.J. Ross, J.M. Sondheimer (Eds), CURRENT Diagnosis & Treatment: Pediatrics, 21e.