I pretty much only use the terrain for Alpha Strike games, so not sure yet on how to handle transition hexes.
For the slopes, there can be some stability issues for top heavy or large plastic models. They do not slide however, as the flocking gives the base grip.
Some plastic miniatures will topple on the slopes, particularly those with those truncated, Alpha Strike bases. For that reason it's a good idea to glue a coin or washer on the underside of the plastic hex base to make them more bottom heavy, or re-base them on normal hex bases. All metal miniatures typically handle the slope without issues as the metal hex base and the model weight keeps things stable.
One thing you will need, when using the terrain, is some kind of border to prevent the terrain from sliding around the tabletop. There are corner slots for card tabs that are supposed to help keep the terrain together and stable, but they are pretty useless. So a dedicated gaming table or table topper with a raised border is pretty much required.
The typical, required size for such [for Alpha Strike as well as most tabletop games like Warhammer, etc.] is going to be 4x6 feet. Or I suppose one could try to build an improvised border for a normal table, like a taped on cardboard frame. The table dimensions then should be in multiples of 6" to fit the hexes.