This paper is concerned about the impact of network parameter errors on the reliable operation and management of electricity markets. Specifically, the paper investigates the so-called critical parameters in a network model whose errors cannot be detected or estimated due to the lack of local measurement redundancy. Due to this property of critical parameters, it will be impossible to detect, identify and correct errors in these parameters. Given the fact that electricity market applications are heavily model-dependent, the locational marginal prices (LMPs) can be shown to be seriously distorted in the presence of critical parameter errors. Furthermore, if such errors are maliciously injected by adversaries, they will go undetected. Meanwhile, prices and revenues associated with power transactions may be strategically manipulated. An approach for quantifying the impact of critical parameters on the management of electricity markets is proposed. Conditions related to network topology and measurement configuration leading to the appearance of critical parameters are classified, and meter placement strategies for avoiding critical parameters are presented as well. Simulation results obtained by using IEEE test systems are given to verify the proposed analysis and design methods.