There are plenty of possible causes for a misfire in an 1.8T. Bad coil, clogged injector, poorly adjusted throttle butterfly, poor fuel rail pressure, cam chain tensioner out of adjustment and so on.
However, they all occur seldomly. Unless the car had poor coils from the factory, as there was a recall just for the coils.
There is one cause which bugged plenty of people and it's actually very easy to cure: poor fueling at high rpm and high boost. When boost jumps over 1.1-1.2 bar at high rpm, it either bucks violently, or misfires like a cannon and then runs slightly better.
Cause? The battery.
Fuel pump relay is made to drive the pump at maximum amps and therefore maximum flow when voltage and current draw are correct and only then. Poor voltage, poor alternator performance leave the car running rather good at normal traffic rpm, but unable to draw fuel at high boost. On Torque app, one can see the A/F ratio jumping madly (too much air, not enough fuel) and then falling back to 14.75:1.
Once the battery is removed from the car and charged properly, high boost fueling is normal again.
The stealer may charge the poor fellow a bucketload of money to change randomly fuel system and ignition parts, and the engine still won't perform until the battery is fresh.