The big one is probably the lag introduced to the control loop by the current sense IC. A lot of those have fairly poor bandwidth, combined with a relatively high frequency switcher that could eat too much phase margin and cause loop stability problems in current regulation mode. Since the current loop will be slower than the voltage loop (because the current loop is just the voltage loop but with more stages in the feedback path) you'll need to figure out a way to compensate the former without (ideally) slowing down the latter too much.
If you're thinking of using a voltage divider from the output of the current sense amp and then a diode from the output of that divider to the FB pin then of course the impedance of the current feedback divider needs to be substantially lower than the impedance of the voltage feedback divider, otherwise the current feedback can't sufficiently override the voltage feedback. You could add an additional op amp as an error amp with one input from the current sense amplifier, the other input from a voltage representing the current setpoint, and the output driving the FB pin via a diode to solve the impedance problem, substantially eliminate the diode Vf from the equation, and maybe make it a bit easier to set the current limit. This would incur additional phase lag in the current regulation loop, but probably less than the current sense amp does. Since the op amp will be saturated when the current is less than the setpoint you'll need to select an op amp that can come out of saturation and back into linear operation quickly if a fast response to overcurrent is important.