You shouldn't even be looking at the current specification of a MOSFET, that's not relevant to practical
use. The on-resistance is what you need to go by - calculate the dissipation by I-squared-R and see if
its reasonable, if not pick a device with a lower on-resistance.
The max continuous current rating is usually a maximum power rating in disguise - at maximum power
a device may need to be water-cooled - its not practical, no-one does it.
For instance if a device says 80A, 0.02 ohms, it will be good for about about 15A with a moderate sized
heatsink (5W dissipation).
If you try to use it at 80 amps it will drop 1.6V (meaning the gate voltage has to be 1.6V higher than
its nominal value), and dissipate about 130W. That would mean a large CPU cooler or similar to keep it
from frying. Pick a better device or parallel them up.
Also you have to watch for datasheets that quote the theoretical max current (ignoring the limit
for the package and bond-wires). IR seem to like specifying a TO220 MOSFET at 290A or something
crazy.
So in summary, check the drain/source voltage, the gate drive voltage (ie logic level or not), and the on-resistance. That's all you really need to consider for reliable on-behaviour.
Note that BJT's max current is different, it is a current limit, not a power limit, so if you are used to
BJTs MOSFETs can be confusing.