Planck Time
There may be some some size below which any smaller distance is meaningless, a granularity inherent in the universe, pixel size is a good term for it. We know there is already a minimum dimension in 6-D phase space (three space and three momentum coordinates) where only one particle in a given quantum state is allowed to exist by the Pauli Exclusion Principle.
I know for a fact there is a minimum allowable time interval in nature: it is the amount of time elapsed between the changing of the traffic light to green and the guy behind me leaning on his horn.