Anybody had this problem, if so what's the solution? I want to make sure the dealer gets the problem fixed in the first try.

The CEL in my wife's RX-8 came on today for the first time. The trouble code is DTC P1416 (read off my CarChip datalogger, which doesn't supposedly support the ODBII CAN protocol).

In five trips, the CarChip logged the same exact problem each trip. The software gives the following data on the DTC:

View / Vehicle Trouble Log / Record Problem 5
Overview
Time : 3/23/2004 6:07 AM
Vehicle : 2004 Mazda RX-8
CarChip : CarChip E/X
Trouble Code : P1416
Description : Unknown Powertrain DTC( Manufacturer Controlled; Auxiliary Emission Controls)
Comments :
Engine Status
Fuel Pressure (Gage) :
Intake Manifold Pressure (Absolute) : 4.5 psi
Engine Coolant Temperature : 165.2 °F
Calculated Load Value : 8.2 %
Engine Speed : 1,612 RPM
Vehicle Speed : 40 MPH
Fuel Trim Status
Short-Term Fuel Trim (Bank 1) : 50.00 %
Short-Term Fuel Trim (Bank 2) : -30.47 %
Long-Term Fuel Trim (Bank 1) : -1.56 %
Long-Term Fuel Trim (Bank 2) : -0.78 %
Fuel System Status
Fuel System 1 Status : Open loop due to driving conditions (power enrichment, deceleration enleanment).
Fuel System 2 Status : Open loop due to driving conditions (power enrichment, deceleration enleanment).

Take it to the dealer to have it looked at..

looking at other OBD-II codes, it could be something to do with the airpump, but that's just a guess based on searching for "obd P1416" on google.

Your best bet is to take it to the dealer and have them check it out.

There is no P1416 on the RX-8.
The closest I could find was P0461, which is a fuel gauge condition (estimated fuel economy does not match the fuel sender level).
P0410 is secondary air, when you start a cold engine you should hear the air pump operating. If it is not operating though, you should have a lot more DTCs though, because the air/fuel mix will be out of spec.
Hope this helps