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Mooring systems exhibit high failure rates. This is especially problematic for offshore renewable energy systems, like wave and floating wind, where the mooring system can be an active component and the redundancy in the design must be kept low. Here we investigate how uncertainty in input parameters propagates through the mooring system and affects the design and dynamic response of mooring and floaters. The method used is a nonintrusive surrogate based uncertainty quantification (UQ) approach based on generalized Polynomial Chaos (gPC). We investigate the importance of the added mass, tangential drag, and normal drag coefficient of a catenary mooring cable on the peak tension in the cable. It is found that the normal drag coefficient has the greatest influence. However, the uncertainty in the coefficients plays a minor role for snap loads. Using the same methodology we analyze how deviations in anchor placement impact the dynamics of a floating axi-symmetric point-absorber. It is shown that heave and pitch are largely unaffected but surge and cable tension can be significantly altered. Our results are important towards streamlining the analysis and design of floating structures. Improving the analysis to take into account uncertainties is especially relevant for offshore renewable energy systems where the mooring system is a considerable portion of the investment.