Cerium 4f electronic spin dynamics in single crystals of the heavy-fermion system CeFePO is studied by means of ac susceptibility, specific heat, and muon-spin relaxation (μSR). Short-range static magnetism occurs below the freezing temperature T_g ≈ 0.7K, which prevents the system from accessing a putative ferromagnetic quantum critical point. In the μSR, the sample-averaged muon asymmetry function is dominated by strongly inhomogeneous spin fluctuations below 10K and exhibits a characteristic time-field scaling relation expected from glassy spin dynamics, strongly evidencing cooperative and critical spin fluctuations. The overall behavior can be ascribed neither to canonical spin glasses nor other disorder-driven mechanisms.