When this collective advises an "Other or considering FJR" we rarely talk about major systems because they are just fine, we all seem to pick on the little things like some of the ones you mention. Everybody perceives things differently, what is unbearable to one person may be totally unnoticed or even loved by another. With that bit of verbal dancing done, on with one person's opinion.
First see Ignacio's
FJR1300 Model Comparison Matrix Also, see my idea of problem definitions at the end of this post.
The '06/'07 share the eccentric throttle pulley that causes the rate of RPM change to be non-linear, which is fixed by a G2 throttle tube. The '06/'07 were included in the ECU recall for altitude drivability issues. The '06 instrument panels on some early bikes were recalled for an instant MPG readout stuck at 17 mpg.
Separate from the non-linear throttle response is abrupt power delivery. Some bikes are worse than others, some riders are more sensitive than others. This is remediated for sure with a PCIII. Some people claim that changing the CO setting helped them. Search out the Barbarian Jumper that enables the CO settings to be adjusted.
No FJR
has to have any of these modifications done or parts added, but when required the G2 throttle tube, a PCIII and perhaps unwinding the throttle spring one turn are sure fixes.
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Surging: At a steady throttle, light engine load, the engine speed varies a small amount which feels like the throttle is being opened and closed a tiny amount even though it is being held steady. Sometimes fixed by CO adjustments, fixed with a PCIII.
Abrupt power delivery: When the throttle is closed the engine goes into a decel FI routine where fuel injection is basically turned off, then when power is asked for again there may be small hesitation without response as the throttle is rolled on, then suddenly you get all the throttle that you dialed up. Helped/fixed by a PCIII
Abrupt Throttle Response II: The Gen II throttle cam is eccentric (not round) causing the throttle to respond in greater proportion than what the operator intended. The steep ramp of the throttle cam is right around the 3k rpm range. A second issue are the gorilla springs on the throttle pulley making it very tiring to use and makes fine throttle control difficult. A G2 throttle tube & cam will neutralize the eccentric throttle cam. Some people acknowledge the risks and partially unwind the throttle springs to lighten up response.
Drive line lash: Free play between the engine output shaft and the rear wheel. With the bike on the center stand, engine off, in gear, rotate the rear wheel and note how much free rotation it has. This could possibly cause the same feel as abrupt power delivery and/or surging. No fix, not proven to be an issue.
Altitude sickness: Total lack of throttle response, bogging, very poor drivability. Often initiated by rapid altitude change, often reset back to normal operation by cycling the key off/on. ECU recall.
Buzz: Rapid mechanical vibrations, usually felt in the bars and pegs first and as it gets stronger the frame & tank. There is a common rpm range someplace between 4k rpm and 6k rpm. It is not unusual for some bikes to buzz at one rpm and another bike at a different rpm but the buzz is almost always in a range that you can pass through and get smooth operation again.
Buzz can usually be all but eliminated with a good throttle body sync (TBS). There are a lot of other tweaks, like fuel management via a Power Commander III that can be done to help too. Sometimes loosening the engine mounting bolts and retightening will get stubborn buzz to quit. Don’t do the engine bolts without the service manual’s specific order. Bar end weights and Grip Puppies are a way to manage residual buzz.
