While I've seen some of the Planck units, such as the Planck Distance and Planck Time, being described as the smallest values that make any sense in QM, some of the other (derived) Planck units are quite large, and the Planck Temperature represents a maximum rather than a minimum value, so it must be possible to work with sub-Planck unit values. This seems contradictory to me.

There also seems to be another practical problem, regarding the Planck Distance and Time units, in that working with sub-light speed values requires using values of < 1 Planck Distance/Time. For a large object, composed of many particles, I could see how its average speed could be < c by statistical averaging of each of the individual particles velocities but when you consider the movement of a single particle you hit problems, especially if the particle is accelerating/decelerating.

If you consider a very slowly moving particle, it seems to me that it must either be constantly moving over either < 1 Planck Distance for each Planck unit of time, or it must take a varying number of Planck units of time to move one Planck Distance unit. At high speeds though, even taking a varying number of Planck Time units to move a single Planck Distance unit is problematic; when traveling at 0.5 c you'd take two Planck Time units to travel one Planck Distance, which is fair enough, but then what happens when you travel at 0.75 c? You then need to deal with fractions of Planck Time units.