Mt Mulligan has very very very soft rock. Like really crazy soft rock.
Chillago is bloody hot all the time and the limestone seems quite fragile.
Mossman gorge looks fantastic, the trouble is actually finding the route and the way in. Would be great to hear from the guys who put the route up originally.
Baron gorge is great. Fun climbing. I believe the area is currently closed to climbers (however that never really stopped anybody. Last time I went down there the walking track was a little overgrown. You can only really climb in winter because in summer the whole place is under water.
There are various other places to climb around Cairns, however most of them are much easier to do if you have a local the guide you around. I grew up in this area, but I currently live in Brisbane.
There is also a tone of potential for climbing on the Atherton tableands, however it is winter only and you would need a 4WD to get access to it.