Time-resolved magneto-optical studies are performed on MgB2 thin film samples grown by in situ pulsed laser deposition and in situ reactive deposition technique. The latter reveal dendritic avalanche-free flux penetration. The kinetic roughening of magnetic flux penetration is studied for applied ac current. Dynamic scaling laws determined for both static field and ac current are consistent with the directed percolation depinning model, placing the vortex dynamics in MgB2 in the same universality class as YBCO and Nb. (c) 2007 American Institute of Physics.