Markov state models (MSMs) are employed extensively in literature with the kinetic Monte Carlo (KMC) method for studying state-to-state dynamics in a wide range of material systems. A MSM contains a list of atomic processes and their rate constants for different states of the system. In many situations, only few of the possible atomic processes are included in the MSM. The use of an incomplete MSM with the KMC method can lead to an error in the dynamics. In this work, we develop an error measure to assess the accuracy of a MSM generated using dynamical basin escape pathway searches. We show that the error associated with an incomplete MSM depends on the rate constants missing from the MSM. A procedure to estimate the missing rate constants is developed. We demonstrate our approach using some examples.