IIRC DPF was introduced somewhere around 2007...
Be sure to check the condition of the main ground wire from the battery to the engine block. FIAT cut some ugly corners here by omitting the usual ground strap from block to body. A corroded main ground wire will result in some badly burned other ground wires inside the engine cable harness, as the cranking current will try to find other ways from the block back to the negative post of the battery. Having to replace the engine wiring harness is an absolute bitch!
Body and drive train are generally solid. Stay away if second gear is hard to engage and / or noisy when cold - this means that the synchronisers of that gear have not been replaced under warranty as they should have been.
Wiggle the front stabilzer links - they are a bit on the spindly side and need replacing after a few years.
The fuel lines under the car are metal and prone to rusting if the surface has been scratched by lots of offroading or driving over chunky snow. Having them replaced is not exactly cheap.
The seal of the rear differential input shaft won´t last the car´s life - check for oil on the outside of the housing. Easy to fix though.
Glow plugs will only last some 100000 km or so. Check for Preheating system error with
MES, that usually indicates one of them is gone.
If the oil pressure warning light is flashing after the engine has started the owner has not had the oil degradation counter reset at servicing. This means the DPF regen cycle will have been pushed back to lessen oil thinning. If the car has been driven like this for years there will likely be DPF problems.
If the engine shudders at shutdown the EGR valve is stuck open. Most of the time this means a new EGR valve and a very messy job cleaning the whole intake system of carbon deposits.
With a warm engine, take it for a spin on the motorway, floor it in third and look into the rear view mirror. If you see a big cloud of black smoke (a small puff is normal) either a hose on the turbocharging system is split or the intake is badly gunked up.