I bought a 2005 S type R about 4 months ago and so far so good. One thing I have noticed is when I turn the engine off after I have been driving for a while I hear what sounds like a faint gurgling from behind the dash more on the passenger side. Is this air in the coolant or something else I should be concerned about?

 

Normal, there are many threads to explain why it happens.

Welcome to the forums!

 

I've never heard a gurgling noise. Sounds haunted.

 

I'd suggest getting out of the car more quickly or turning up the radio if you plan to sit a while. That should take care of it.

All seriousness aside, is the coolant level okay? If low, you may get some air in the heater lines. Does the heater and AC work okay? If the coolant level and HVAC operation are okay, I wouldn't worry about a faint noise after shutdown. There's an official bleeding procedure for the cooling system, but it's something of a pain. Usually just normal driving of the car purges the air from the lines. If you haven't been driving much, or just babying the car, the air may not have fully cleared itself. If still concerned, you can always do the full bleeding.

 

This is likely the actuators attached to the louvers of the ducts that are part of the heating and cooling system stuck in a cycle of opening and closing repeatedly. It's a known fault and dealers got a shop notice on this for 2004 to at least 2006 S-Types to recall and repair at dealers expense. I had to fight with my dealer but they finally relented and replaced the faulty parts at their expense, including labor. Best of luck.