We describe an ordinary Poisson list-mode expectation maximization (OP-LMEM) algorithm with a sinogram-based scatter correction method based on the single scatter simulation (SSS) technique and a random correction method based on the variance-reduced delayed-coincidence technique. We also describe a practical approximate scatter and random-estimation approach for dynamic PET studies based on a time-averaged scatter and random estimate followed by scaling according to the global numbers of true coincidences and randoms for each temporal frame. The quantitative accuracy achieved using OP-LMEM was compared to that obtained using the histogram-mode 3D ordinary Poisson ordered subset expectation maximization (3D-OP) algorithm with similar scatter and random correction methods, and they showed excellent agreement. The accuracy of the approximated scatter and random estimates was tested by comparing time activity curves (TACs) as well as the spatial scatter distribution from dynamic non-human primate studies obtained from the conventional (frame-based) approach and those obtained from the approximate approach. An excellent agreement was found, and the time required for the calculation of scatter and random estimates in the dynamic studies became much less dependent on the number of frames (we achieved a nearly four times faster performance on the scatter and random estimates by applying the proposed method). The precision of the scatter fraction was also demonstrated for the conventional and the approximate approach using phantom studies.