This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with focus on Massive MIMO. This distortion is correlated across the antennas, but has been often approximated as uncorrelated to facilitate (tractable) SE analysis. To determine when this approximation is accurate, basic properties of distortion correlation are first uncovered. Then, we separately analyze the distortion correlation caused by third-order non-linearities and by quantization. Finally, we study the SE numerically and show that the distortion correlation can be safely neglected in Massive MIMO when there are sufficiently many users. Under i.i.d. Rayleigh fading and equal signal-to-noise ratios (SNRs), this occurs for more than five transmitting users. Other channel models and SNR variations have only minor impact on the accuracy. We also demonstrate the importance of taking the distortion characteristics into account in the receive combining.