Thermochromic VO2 films were prepared by reactive DC magnetron sputtering onto heated sapphire substrates and were used to make 100-nm-thick samples that were 10 μm wide and 100 micron long. The resistance of these samples changed by a factor of about 2000 in the 50 < Ts < 70 C range of temperature Ts around the "critical" temperature Tc between a low-temperature semiconducting phase and a high-temperature metallic-like phase of VO2. Power density spectra S(f) were extracted for resistance noise around Tc and demonstrated unambiguous 1/f behavior. Data on S(10Hz)/Rs^2 scaled as Rs^x, where Rs is sample resistance; the noise exponent x was -2.6 for Ts < Tc and +2.6 for Ts > Tc. These exponents can be reconciled with the Pennetta-Trefán-Reggiani theory [C. Pennetta, G. Trefán, and L. Reggiani, Phys. Rev. Lett. 85, 5238 (2000)] for lattice percolation with switching disorder ensuing from random defect generation and healing in steady state. Our work hence highlights the dynamic features of the percolating semiconducting and metallic-like regions around Tc in thermochromic VO2 films.