Antialiasing particles, both spatially and temporally, can be an important consideration, especially if particles are moving slowly. Antialiasing points will cause the particles to move more smoothly as they cross pixel boundaries, since fragments with fractional alpha values will be generated. Another technique is to use the particle positions between two adjacent frames to orient a line centered at the particle's current position, and draw an antialiased line instead of a point. If the line's length and alpha are varied as a function of current velocity, you can create a motion blur effect.
If high quality is important and performance is not, or you have very good hardware support, the accumulation buffer can be used to generate excellent antialiasing and motion blur. The particles for a given frame can be rendered repeatedly and accumulated. The particle positions can be jittered for spatial antialiasing, and the particle re-rendered along its direction of motion can produce motion blur effects. For more information, see Section 9.5 in these notes, and the accumulation buffer paper in the 1990 SIGGRAPH Proceedings  reprinted in these course notes.