Movement of particles in cell nuclei can be affected by viscosity, directed flows, active transport, or the presence of obstacles such as the chromatin network. Here we investigate whether the mobility of small fluorescent proteins is affected by the chromatin density. Diffusion of inert fluorescent proteins was studied in living cell nuclei using fluorescence correlation spectroscopy (FCS) with a two-color confocal scanning detection system. We first present experiments exposing FCS-specific artifacts encountered in live cell studies as well as strategies to prevent them, in particular those arising from the choice of the fluorophore used for calibration of the focal volume, as well as temperature and acquisition conditions used for fluorescence fluctuation measurements. After defining the best acquisition conditions, we show for various human cell lines that the mobility of GFP varies significantly within the cell nucleus, but does not correlate with chromatin density. The intranuclear diffusional mobility strongly depends on protein size: in a series of GFP-oligomers, used as free inert fluorescent tracers, the diffusion coefficient decreased from the monomer to the tetramer much more than expected for molecules free in aqueous solution. Still, the entire intranuclear chromatin network is freely accessible for small proteins up to the size of eGFP-tetramers, regardless of the chromatin density or cell line. Even the densest chromatin regions do not exclude free eGFP-monomers or multimers.