Standard Omega problems are : Rust around rear wheel arches ( remove rear plastic covers near side skirts for detail inspection), bulkhead around steering column ( rust can bee seen from inside if you remove carpet, or from outside if you lift plastic cover beneath windscreen wipers)
Front suspension is weak ( especially with heavy 3.2),
When testing auto gearboxes, I usually drive it slowly first, and look how it shifts. If there is hesitation while shifting usually there is a problem ( how big that's hard to say). Most of the auto gearboxes perform ok when pushed hard but they show first signs of problem when they are driven lightly. Off course, you get it's temperature up first.
V6 problems are common across the whole range, so it's same story as for your Calibra. ( oil cooler, cam cover gaskets, head gaskets, exhaust manifold gaskets etc). And they drink fuel like Merc S 500 uphill towing a trailer
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