There really aren't any real specific differences between surveying a monohull or a catamaran or trimaran. The systems on the three are pretty similar and will likely have the same issues for the most part.
There are a few multihull specific issues that you'd need to check specifically.
Catamarans:
The steering is usually two rudders, one on each hull, and that complicates the steering setup a bit, with additional cables or linkages.
There are often two engines, two cutless bearings, two prop shafts on a catamaran. This complicates the electrical setup slightly and gives you more to inspect in terms of engine and propulsion.
Also, there are generally no keel bolts or hull-keel joins to worry about. Instead the hull-to-bridgedeck connection has to be inspected. In many designs, the hulls and bridgedeck are a single composite piece, with no fasteners or real "join" to speak of.
The rigging may often be simpler, with a spreaderless rig due to the wider stay base available on a catamaran. Some may have a rotating mast, which is a bit more complex and requires a bit more investigation and inspection.
Other than that, there really aren't any major differences between a cruising catamaran and a cruising monohull, in terms of things to watch out for.
Trimarans:
The biggest issue on trimarans is on the smaller sport trimarans that fold, since the folding system has its own complexities and mechanical problems. However, the aka structure and how well it has been maintained is a concern on many trimarans, and needs to be investigated.
These also may have a rotating mast, which is unusual on a monohull. Some may have simpler rigging without spreaders, but the folding boats generally have the rigging on the main hull and are rigged much like monohulls.
Many trimarans use an outboard motor as an auxiliary engine, and while that simplifies the inspection process, it also reduces the options for things like A/C, refrigeration, battery charging and hot water.
I read your guide to buying a boat, and it was excellent. Thanks for that resource. Just wondering if there is something similar for catamarans. They seem to have their own unique problems. Have you thought of putting together something for us buyers who want a pre-survey inspection of a cat?
MediaGuy