Refers to the potential for genetic variants (including SNPs) to associate with multiple phenotypes.
The relevance of a SNP being pleiotropic to an MR study is context specific. If the SNP is pleiotropic because it influences the outcome only through an exposure (trait A), this is known as vertical pleiotropy and is the exact phenomenon that MR seeks to detect. The same variant could associate with another exposure (trait B) while only influencing the outcome through (trait A). In the MR analysis of trait B on the outcome, the variant is exhibiting horizontal pleiotropy resulting in violation of the exclusion restriction and, hence, bias of the MR effect estimate.

References
- Davey Smith G, Hemani G. Mendelian randomization: genetic anchors for causal inference in epidemiological studies. Hum Mol Genet 2014;23:R89-R98.
- Zheng J, Baird D, Borges MC et al. Recent Developments in Mendelian Randomization Studies. Curr Epidemiol Rep 2017;4:330-345.
Other terms in 'Sources of bias and limitations in MR':
- Assortative mating
- Canalization
- Collider
- Collider bias
- Confounding
- Dynastic effects
- Exclusion restriction assumption
- Harmonization failure (in two-sample MR)
- Homogeneity Assumption
- Horizontal Pleiotropy
- Independence assumption
- InSIDE assumption (in two-sample MR using aggregate data)
- Monotonicity assumption
- MR for testing critical or sensitive periods
- MR for testing developmental origins
- No effect modification assumption (Additional IV assumption)
- Non-linear effects
- Non-overlapping samples (in two-sample MR)
- Overfitting
- Population stratification
- Regression dilution bias (attenuation by errors)
- Relevance assumption
- Reverse causality
- Same underlying population (in two-sample MR)
- Statistical power/efficiency
- Vertical Pleiotropy
- Weak instrument bias
- Winner's curse