Reliable record linkage is a prerequisite for high-quality population-based disease registration. Rapid developments in computer processing have made record linkage both more efficient and more reliable in recent years. At the same time, concerns about confidentiality increasingly hinder record linkage in many disease registries. This paper provides basic algebraic models describing the effects of record linkage errors on monitoring disease incidence. Homonym errors, that is, erroneous linkage of records that pertain to distinct individuals, lead to underestimation of incidence in the registry population. The degree of underestimation strongly depends on the discriminating power of personal identifiers and the record linkage procedure on the one hand, and the number of registered cases on the other hand. Synonym errors, that is, failure to link notifications on the same individual, lead to overestimation of incidence in the population base. The combined effects of record linkage errors are illustrated with empirical examples. We conclude that it is the largest and most informative disease registries that are potentially affected most by impediments of record linkage procedures due to unduly restrictive confidentiality rules.