In power grids, a critical parameter is a type of network model parameter whose error is not detectable due to the existing measurement configuration. In this paper, the effect of incorrect critical parameters on the calculation of locational marginal prices (LMP) will be investigated. Such errors will present a security vulnerability in the operation of electricity markets. It will be shown that model parameter errors can severely bias LMPs by affecting the injection shift factors (ISFs) and congestion patterns. If the error is undetectable, as is the case for a critical parameter, economic interests of the market participants will be compromised. This implies that it may be possible for potential adversaries to manipulate electricity market operations if they have access the network data base and can manipulate critical model parameters. Simulations on an IEEE test system will be used to illustrate the identified security vulnerabilities related to critical network parameters.