An inverting a 2-stroke can make it easier to get a hydraulic lock situation when using an electric starter. This can lead to engine damage, usually a bent or broken rod, as I understand it. But I've honestly never seen it actually happen.

It can be harder to start, since primeing can be harder, and any excess fuel and oil can have a tendancy to stay there.

On the "plus" side, if your tank is mounted too high and you get syphon action, it won't fill your engine with fuel, it will all train out the carb opening and on to the ground instead. However, with an upright engine, the syphoning usually stops when the engine fills. It's possible to empty an entire tank on to the ground with an inverted engine (and even some side mounted engines).

Once the engine is running and warmed up, I've never noticed a difference.