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A key component to understanding the brain is determining the influence of groups of neurons on each other relative to other influences. In the brain, all neurons are driven by the activity of other neurons, some of which may be simultaneously recorded, but most are not. As such, models of neuronal activity need to account for simultaneously recorded neurons and the influences of unmeasured neurons. This can be done through the inclusion of model terms for observed external variables (e.g., tuning to stimuli), observed internal variables (e.g., coupling to recorded neural activities), as well as terms for latent sources of variability. Despite broad utilization, however, evaluation of systematic errors during inference is rarely performed, and sources of systematic error are poorly understood. Through extensive numerical study and analytic calculation, we show that common inference procedures for static and dynamic models typically have systematic errors. Counter to common intuition, we found that model non-identifiability contributes to systematic errors in parameter estimation, not variance inflation, making it a particularly insidious form of statistical error. We demonstrate that accurate parameter selection before estimation resolves model non-identifiability and mitigates the associated systematic errors. In diverse neurophysiology data sets (multiple single unit recordings in primary visual cortex and hippocampus, ECoG from primary auditory cortex), we found that common methods typically overestimate the contributions of interactions between neurons, while the influence of exogenous variables is underestimated. Essentially, when there are positive correlations due to unobserved shared variability, estimated coupling amongst neurons will be inflated at the expense of tuning. We explain heterogeneity in observed systematic errors across neurophysiology data sets in terms of data statistics and experimental design. Together, our results identify the causes of statistical errors in structural equation models of simultaneous systems with endogenous, exogenous, and latent variables, provide inference procedures to mitigate those errors, and reveal and explain the impact of those errors in diverse neural data sets.