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Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process and under- or over-estimation of this number may lead to incorrect unmixing for unsupervised methods. Most methods for estimating the intrinsic dimension require an estimate of the noise in the image, and noise estimates are often inaccurate in the presence of spectrally correlated noise. Since hyperspectral images are known to contain such correlated noise, intrinsic dimension estimations may be overestimated. In this paper we discuss the effect of correlation, as well as possible methods for overcoming such limitations. For instance, correlated bands may be removed prior to noise estimation, or spatially-based noise approximation methods may be used in place of statistical methods. These suggestions are implemented on synthetic and real images, including images acquired by AVIRIS, Hyperion and SpecTIR.