I bought a filter for my 2003 mitsubishi spyder. It looks like an oil filter rather than the common transmission "flat filer". I can't find this filter on the outside of the transmission. Is it by chance on the inside?

Yes - that filter requires you to remove the transmission pan - the one with all the bolts holding it on - about 20 of them - it will seem like 100 - also replace the gasket too - filter and gasket and fluid - all at the same time frame

Unfortunately the filter for the automatic transmission is inside the transmission case and it would have to be disassembled completely. These are the "lifetime" filter designs.