What it comes down to is this: The force that is accelerating the dishes across the table is _friction_ (between the dishes and the tablecloth); and friction alone can accelerate dishes only so fast. In fact, you can quantify this. Associated with any pair of materials (say, glass and linen), there is a number called the "coefficient of static friction" (μ_s). If you try to use the friction of material "A" to drag an object of material "B" horizontally, the fastest acceleration you can manage, without slipping, is (μ_s)×g, where "g" is the acceleration due to gravity (a.k.a. "one-g", 9.8 meters/sec²). Imagine an (unsecured) box in the bed of a pickup truck. If the truck pulls away from a stop at a relatively low acceleration (lower than (μ_s)×g), the box won't slip. But if the truck accelerates too fast, the box slips backwards, because the truck bed can't generate enough friction force to accelerate the box at that higher acceleration.
It's the same with the tablecloth. If you accelerate it slowly (slower than (μ_s)×g, where "μ_s" is the particular coefficient for the dishes and the tableloth), the friction between tablecloth and dishes will be enough to prevent them from slipping. But friction alone can't accelerate them faster than that, so a "fast pull" will leave them behind.