The marketing "power dissipation" numbers are quite irrelevant, particularly for high power parts. Instead, look at thermal resistance and permissible junction temperature and do the math.
Don't forget about case-to-sink resistance, which appears to be the primary limiting factor with very large FETs, assuming that those "typical" numbers I collected from various appnotes but never really tested myself are anything to go by:
TO264 .15 K/W
TO247 .21 K/W
TO220 .40 K/W
The above table really cooled my enthusiasm for 2kW devices with .0x K/W specs.
Regarding offset voltage, it really depends if it's positive or negative. If at least one opamp ends up regulating its IN- to slightly higher than its IN+, you will never be able to get the current down to absolute zero. A simple solution to that is to allow the IN+ voltage to go slightly below ground. Furthermore, between any two sections, current imbalance will be equal the difference of their opamps' offset voltages divided by 50mΩ.
edit
Please elaborate on the 'nasty case', I am not sure what you mean about turning down the mosfets. The way I have been using my loads to to make sure everybody is at minimal voltage and current settings, power supplies and loads, before connecting and powering on (and when shutting down).
It's simple. If the load is set for 1mA current but there is no PSU and therefore 0mA current, the opamps will apply full 15V to the gates. There will be a high inrush current until the opamps recover from saturation and discharge the gates down to the linear region. If the PSU has too much output capacitance perhaps the FETs may blow up, if its short circuit protection isn't as good as you think perhaps the PSU may blow up
So far I have had luck operating such unprotected load myself. It is, however, naturally limited to some 150~200% nominal current by base resistor and beta droop of the power BJT.