* Engine Mounts: The 307 and 350 Chevy small-block engines have different dimensions, meaning the engine mounts will likely need modification or replacement. You'll probably need specific motor mounts designed for a 350 in a Cutlass.
* Transmission: The transmission compatibility depends on the original 307's transmission. A 350 might require a different transmission or at minimum, a different torque converter.
* Exhaust System: The exhaust manifolds and pipes will almost certainly not fit. A new exhaust system will be needed.
* Wiring Harness: The wiring harness may need modification to accommodate the 350's different sensors and components.
* Computer Control: The 1985 model year likely has a computer-controlled fuel injection system. You may need a new computer or a modified one to work with the 350. This is a potentially complex aspect of the swap.
* Cooling System: The 350 is a larger displacement engine and will generate more heat. You may need to upgrade the radiator and cooling fan to ensure adequate cooling.
* Driveshaft: The driveshaft may need shortening or lengthening depending on the transmission choice.
In short, while it's *feasible*, this isn't a weekend project. It requires significant mechanical skills, specialized tools, and potentially custom fabrication. You'll need to source the 350 engine, transmission (if needed), motor mounts, exhaust system, and potentially a new wiring harness and computer. It's also advisable to consult resources specific to Oldsmobile Cutlass swaps for guidance and potential pitfalls unique to your car. Expect to invest considerable time and money.