well.... directional stability, as i call it. My personal pet hate, or the lack of it, in the Omega. Or any other vehicle for that matter.
You can have the most mechanically sound car in the world, and have it drive like jelly on a plate if it has the "wrong" tyres fitted.
Whats the wrong tyres? Whats the right tyres? Falken 912s are the wrong tyres, i'll spare you the story for once. But after a long battle, i was able, with help of another member on here, to swap a pc.pair wheels for a week with Dunlop sports max fitted. A marked improvement.
I was also lucky enough to drive his car with them fitted as well. An mv6 customer spec 3.2 of same year as my 3.2 Elite with very similar miles. His mv6 was a joy to drive, tracked perfectly, suspension rode the bumps instead of deflecting round them, and transmitted what was under the wheels by the suspension, and not the stearing wheel. "It can be done" i thought, what a relief to drive that car. It is possible to get an omega to drive straight.
Trouble with tyres is they are a very individual thing for people. Some, dont notice issues that others do, just doesnt bother them or they simply do not notice. Or, due to price, they will swear blind a tyre is better, purely because its cheaper. Feel good factor can take over and defy all reality.
Sometimes just a quiet tyre can convince you its better, only to find it has less grip in the wet or dry, wears out quicker, and the car degrades into i wobbly pile of pooh....

The manual does state, that not all tyres are suitable for the omega, as i recall. Trouble is, it does not state what tyres ARE suitable. Interesting to note, the omega left the factory with michelin primacy i'm told. Possibly the most expensive tyre available?
And speaking to Tony at Wim. Tyres that work well on one car, can be appalling on another. Something i know to be very true on motorcycles. Seems small cars work quite well with the above mentioned Falken 912s for instance. Front wheel drive may very well have an affect as well.
Of course, mechanical issues are the first place to start. Hth