The 1.4 engines in the 500L don't have MultiAir, so no need to worry.
There's a 1.4 16v 95bhp engine, which is just a non-turbo engine which is used in many other models including some earlier Alfa MiTo's, plus the Fiat Doblo and the first few years of Fiat 500 production. It's not going to set any land-speed records but it's dependable.
There's also a 1.4 T-Jet 120bhp engine, which was only offered in UK spec 500L's for a few months, so is rare, but it's been available as the entry petrol engine in the Giulietta right since the Giulietta was launched, and it was in earlier MiTo's too, as well as some Grande Punto's. Again, a solid engine.
The only engine in the 500L with MultiAir tech is the TwinAir engine, but it's 0.9 litre. Again it was phased out of the 500L a while ago so there's not huge numbers of these around either. The TwinAir engine can have the same issue as MultiAir engines, but it seems to happen less often.
Whichever engine you settle on, make sure you have a good test drive, as the power on offer in most of the engines (except the very rare T-Jet and the 1.6 diesel) is adequate rather than plentiful. Most people seem to have gone for the diesel engines, probably because of their torque, which makes them feel more powerful.
