in essence, most modern cars have knock sensors that retard timing in the event of the predetonation, which is the number one reason to use high octane fuel. the higher the octane, the more the fuel/air mixture can be compressed. generally, higher octane fuels should be used in engines with higher compression ratios. other than additives, there is no reason to use high octane fuels in lower compression engines like my 8.8:1 E30, which sees no difference between regular and premium fuel. however, if may become necessary in lower compression engines like the M20 in my E30 due to carbon build up and other gunk in there. this is because the gunk changes the compression ratio to be higher than standard, causing predetonation. it can be remedied by the use of higher octane fuel or a head job. (dont take that outta context).
this being said, i do not know the compression ratio of the M54B30 that is in the 330Ci. You will have to figure that out, but no, damage would not be had in the short term because the computer will retard the timing which equals lower performance, which you dont care about. HOWEVER, i would not recommend the use of lower octane fuels for long periods of time in an engine with a higher compression ratio.
all these facts ignore the different additive packages that gas vendors put in their gasses. Some argue that the additives placed in the higher octane fuels can help prevent the buildup of carbon and other crap in your combustion chamber, thus giving you the best fuel economy and performance, which i am sure is true to an extent.
that brings up the other point of fuel economy. if the computer retards the timing, then your engine will not be running at best efficiency, thus probably wasting gas and perhaps polluting (if you care about that, im like whatever to a certain extent). so it seems to create a fine line between not being efficient with the lower octane fuel, and being more efficient with higher octane fuel, which again depends on the compression ratio. so thats worth finding out. it should be listed in the owner's manual that comes with the car.