Diesel engines provide more lubricity to an engine on start up, so used to be better for short runs from cold. The problem is that since diesel engines became more efficient and since legislation forced them to emit less they have become less reliable.

Potential problem areas are:

Diesel particulate Filters: £500 - £6,000 if the engine fails

Exhaust Gas Recirculation valves: £100 - £300

Turbos: £750 - £1,500

Intercoolers: £300 - £500

Injection pumps: £1,000 - £2,500

Injectors: £100 - £2,000

Dual Mass Flywheels: £800 - £1,600

As you can see, the cost of rectifying any of these soon exceeds the
benefit of lower fuel costs. Though generally if you do more than 15,000 miles a year the financial gamble is worth taking.