The Jimny is a great car, and a great offroad fun toy. Just watch out for rust, especially in the chassis, wheel arches and the rear floor - poke it all over with a screwdriver.
The early soft top vehicles have a different engine, they have the old G13 engine like the SJ413 and Samurai, but 16 valve and with fuel injection. Hard top vehicles and later soft tops (after 2004?) have the newer M13 engine. They're both pretty cool engines though. If you get an M series engine, make sure you know if it's got VVT or not in case you ever need to replace anything, the non-VVT M13 is not replaceable with the VVT version and vice-versa, although they're all really good engines.
Don't quote me, but I think a 2004 is going to be a non-VVT. If it's a G13, then it's definitely not VVT.
I think sometime in 2004 is when the Jimny got antilock breaks, so if it has those, check if they work - although I don't think there's any known problem with the system Suzuki used.
Check the axles for signs of wear around the welds. It's a known weak point of Jimmys - the welds in the axles can rust out. Poke them, look for rust, look for signs of oil seepage, and if you are in any doubt - walk.
Only other thing I can think of is that the automatic locking freewheeling hubs for the front wheels can go wrong. It's usually a bad vacuum line or pump. It's worth checking if 4wd actually works, the light can come on even if it's not working. Don't try to test 4wd on tarmac or any kind of grippy surface!!!
Suzuki Jimnys don't have a central differential, if you use 4wd on a surface with high grip, you can grenade the drive train.
Oh, and
I think they covered it