Hmmm, '03, rattling noise, left side, getting worse... It may be time to think -- TICKER. Early FJRs had valve stem seals that were too tight causing oil starvation in the valve guides which led to valve guide and valve stem wear. The result was a 'rattling noise'. Once the wear gets bad enough to hear, oil is leaking down into the combustion chamber. Over time Yamaha determined one of the best diagnosis of the problem was to pull the exhaust header and look for traces of oil coating the header. Yamaha used to pick up the cost of removing the cylinder head and machining out the valve guides, then replacing the guides with slightly looser stem seals, new guides and new valves. If this is indeed the source of your rattling you will have to negotiate with Yamaha over picking up the cost. You can use a mechanics stethoscope to listen to the valve train, this will quickly rule out a ticker.
Ok, we have the worst case on the table. Now, do you know if the Throttle Position Sensor has been changed? The beginning of engine misfire because of the TPS wearing out *might* cause the noise you are hearing. The TPS is often temperature sensitive, only malfunctioning when hot and always at the same throttle opening without regard to gear or speed.
If the above and bad gas are ruled out there is an outside chance that the reed valves in the Air Injection System have carboned up and are stuck slightly open or the AIS solenoid is stuck open or has been unplugged. The AIS solenoid is normally open and has to be powered to close. The AIS is supposed to inject air into the exhaust stream only when the engine is cold or once warm, only at idle. This does indeed cause popping in the exhaust during deceleration.
