Factors affecting polarising ability
Positive ions can have the effect of polarising (electrically distorting) nearby negative ions. The polarising ability depends on the charge density in the positive ion.
Polarising ability increases as the positive ion gets smaller and the number of charges gets larger.
As a negative ion gets bigger, it becomes easier to polarise. For example, in an iodide ion, I-, the outer electrons are in the 5-level - relatively distant from the nucleus.
A positive ion would be more effective in attracting a pair of electrons from an iodide ion than the corresponding electrons in, say, a fluoride ion where they are much closer to the nucleus.
Aluminium iodide is covalent because the electron pair is easily dragged away from the iodide ion. On the other hand, aluminium fluoride is ionic because the aluminium ion can't polarise the small fluoride ion sufficiently to form a covalent bond.