Some quick thoughts:
You can calculate a net shear force parallel to the foundation and a net overturning moment on the tank and on the foundation due to the uneven loading, and the results of those will be similar to seismic loading, only as sustained loads.
Once you have that uneven loading, that may promote even more settlement.
A fixed roof might not drain right.
Manways on the down side would be inaccessible.
The tank could float when empty due to rainwater ponding around the down side.
Water ponding around the low part will lead to repad corrosion.
Leak detection tubes may be inaccessible.
Stairs or ladders could be out of plumb, or leaning backwards/outwards in hazardous ways.
Roof columns would have gravity lateral loads, I assume a minor issue, though.
You normally derive hoop tension assuming an axisymmetric loading. I don't know what happens with asymmetric loading. Could you get big buckles in the shell? You'll at least have some big shear loads that are not normally generated.
Bottom may no longer drain to the sump, and could trap several feet of product when the tank is "emptied".
A floating roof will float level, but the hole it's in will now be elliptical.
Capacity is reduced. Gauging tables are useless.
Instrumentation on the uphill side won't show depth on the downhill side and could lead to overfills.