Effective agricultural policymaking requires the accurate estimation of the production technology and efficiency of farms. However, several methodological issues should be considered when modelling production and estimating technical efficiency. In this paper, we focus on two of these—technological heterogeneity and theoretical consistency—as implied in microeconomic theory. Heterogeneity in the efficiency literature is often evaluated using a variable intercept model. However, in farm production, it is likely that heterogeneity also affects the marginal productivity of production factors. Some earlier papers investigated the effect of unobserved heterogeneity on technical efficiency using latent class models, but the application of random parameter models is limited. One of our main contributions in this paper is that we apply a modified version of a random parameter model to investigate the effect of unobserved heterogeneity on production factors and efficiency. The second aim was to impose regularity conditions into the model through introducing linear and non-linear constraints and thereby investigate their significance. Third, we examined the relationship between unobserved heterogeneity and the natural and economic conditions of farms. Our findings show that heterogeneity has a greater effect on variation in output than technical efficiency; furthermore, the violation of theoretical consistency significantly influences the results. These findings also reveal that the explanatory power of regional natural and economic conditions is significant but not sufficient on the variance of estimated unobserved heterogeneity.