I'm not sure there's much on an Omega that's strictly an age related failure. Rubber parts such as bushes perhaps, but I'd bank on the wishbone bushes and rear doughnut bushes needing doing on any 2nd hand Omega and the rest don't seem to have started failing in a big way yet. The last of the Omegas don't appear to have got to the age where rust is a serious issue unless badly neglected, save for the odd bubble on the doors or crispy rear wheel arch, nor degradation of brake lines, rubber hoses and so on.
Tyres, exhausts, crank sensors, HBVs, etc. are consumables, so nothing out of the ordinary to worry about on a low mileage car.
I would look at how it's been serviced. If it hasn't been serviced at least annually, regardless of how low the mileage is, then you can expect problems with the oil cooler, breathers, cam cover gaskets and so on as these are more likely to deteriorate faster if fluid changes have been neglected, especially if the car's only been used to potter around.
Based on how my car drives at 180k, however, I would buy any future Omega based on tidiness of the bodywork, as mileage is really of practically no consequence to the V6 mechanicals, it seems.