It is important to note that the list given above is qualitative and describes trends. The ability of a group to leave is contextual. For example, in SAr reactions, the rate is generally increased when the leaving group is fluoride relative to the other halogens. This effect is due to the fact that the highest energy transition state for this two step addition-elimination process occurs in the first step, where fluoride's greater electron withdrawing capability relative to the other halides stabilizes the developing negative charge on the aromatic ring. The departure of the leaving group takes place quickly from this high energy Meisenheimer complex, and since the departure is not involved in the rate limiting step, it does not affect the overall rate of the reaction. This effect is general to conjugate base eliminations.
Even when the departure of the leaving group is involved in the rate limiting step of a reaction there can still exist contextual differences that can change the order of leaving group ability. In Friedel-Crafts alkylations, the normal halogen leaving group order is reversed so that the rate of the reaction follows RF > RCl > RBr > RI. This effect is due to their greater ability to complex the Lewis acid catalyst, and the actual group that leaves is an "ate" complex between the Lewis acid and the departing leaving group. This situation is broadly defined as leaving group activation.
There can still exist contextual differences in leaving group ability in the purest form, that is when the actual group that leaves is not affected by the reaction conditions (by protonation or Lewis acid complexation) and the departure of the leaving group occurs in the rate determining step. In the situation where other variables are held constant (nature of the alkyl electrophile, solvent, etc.), a change in nucleophile can lead to a change in the order of reactivity for leaving groups. In the case below, tosylate is the best leaving group when ethoxide is the nucleophile, but iodide and even bromide become better leaving groups in the case of the thiolate nucleophile.