Have the dealership pull up an Oasis report, this report will tell you what has been done under warranty in the past. With the '06, the STC fitting was one of the main issues. The original design is faulty.
Most big dealers and shops have scan tools to read engine parameters, or you could borrow/buy a monitor to check things out before you sign the papers. Your gonna want to find out what the FICM volts are while cranking the motor and while the motor is running, any FICM volts below 46v with good batteries is a sign of a failing FICM. A failing/weak FICM can destroy injectors.
Your also gonna want to know what the ECT and EOT temps are. If the difference between the two are more than 15*, you have issues with the oil cooler. A blocked up oil cooler can cause a domino effect and cause headgasket failure.
Fuel pressure is another concern, when psi drops below 45psi, your damaging the injectors.
You can check out these two links, read over them and use the knowledge to go over the intended truck, any issues you find from these links can be used to lower the final cost before signing papers.
What to look for when buying a used 6.0L
Things to consider about owning a 6.0L
This next link can provide insight on issues with certain years, along with issue you may want to address after your purchase.
Write Up: Bullet-Proofing the 6.0L PSD.
The Edge Insight CS/CTS is a good monitor, so is the ScangaugeII. Since you have an iPhone, also consider the DashBoss. If you were to buy the Edge CS/CTS with everything to monitor the 6.0, your looking at $500-$600. For the ScangaugeII to completely monitor the 6.0 it's around $300. With the DashBoss to monitor everything with the 6.0, it's $300.
When I say completely monitor, I'm referring to the additions of EGT and fuel psi.
Here is info on the DashBoss.
DashBoss monitoring review.
2004 F350 CC DRW King Ranch
X-3 tunes by DJ'S,QT,GH,ID. Gryphon FICM tunes, ARP studs,Stage 1turbo,ATS coolant recirc lines,Swamp's 48v ficm,coolant filter,AD2,Snow Perf stage II,EGR delete,4" turbo back straight pipe,S&Bintake,Quad "A" pillar autometer gauges,Suncoast Tri Disk Conv.,Billet input shaft,Suncoast superduty rebuild kit,Trans-go shift kit,Mag-Hytec trans pan,CFM+ elbow,ccv mod,15K reese 5er,17" LCD TV/DVD,Cobra 29 Nitewatch CB