Can I use a toroidal inductor as part of a tuning circuit for medium waves?
A toroidal inductor generally doesn't have a gap in the core and this certainly does increase the inductance for a given number of turns. However, for most commonly used ferrite core materials this will mean that temperature changes will change the permeability of the core and the inductance will rise or fall. This of course means tuning will or can drift. Here are a couple of common materials from ferroxcube: -



A gap significantly lowers the effective permeability of the core and this also significantly reduces the temperature dependency. You also have to find a core that is suitable for AM radio frequencies (about 1 MHz) and this is by no means a given for every core material: -



So what you want is a material that remains fairly flat across the band you want to operate in.