The problem you're talking about it caused by the communication lag between the wheel's ff unit, and the game. Every steering wheel has a lag between when you turn it, and when the ps2 notices you've turned it (and then sends the relevant info back). The GTP lag prediction code must've been whacked out.
Seems a few controller issues were predominant in GT
and were subesquently fixed in the new version (along with the ff turning off etc..).
So, no, it's not speed wobbles (cars dont get speed wobbles unless they have no shock absorbers, especially high downforce cars!).
Road cars are a lot less twitchy than race cars. Road cars have these things in them called rubber bushings, which are replaced by either hard bushings or rose joints (the original GT40 had rose joints throughout, made it very harsh to drive, but very direct). They also have a slower rack than race cars, softer dampers, slower action tyres, etc etc.
The modern Ford GT doesnt have as much lift as the original. It has a front spoiler (small strip under the front), which significantly cuts the lift of the car when coupled with several other modifications to the body/underpan.
So it looks like the high powered cars in GT4 will be driveable then (err, relatively).