Idle problems are often associated with a dodgy PCV, and a bad injector can also cause a very lumpy idle as well as misfires and a lack of power under load.
The PCV should really be checked and if necessary replaced along with a service; even though VW don't deem it a serviceable item, they often fail. You can list the diverter valve and cam follower in that category too.
First off, with the engine idling pull the oil dipstick. If the engine doesn't change in the way it's idling it's a fair indication that the PCV has seen better days. Usually with a good PCV, pulling the dipstick will cause the engine to idle badly. Put the dipstick back in, and a good idle is restored.
If that fails, I'd get it scanned. Any fault codes might give you a starting point. But be mindful that the lack of a code doesn't necessarily indicate the lack of a fault. One step better than a code scan is live data logging with VCDS. If you're paying a garage to do the diagnostics with VCDS the cost will soon start adding up. It'd help if you knew a friend or fellow forum member with VCDS!