Yes, that's correct, kajoh, the R3 did have some bad parts and production issues, predominantly into about the first half of the '07 model year run. I am certain that several members will come along to provide more detail, however you should be able to find all of the pertinent info by utilizing the search function on the main toolbar above. "Factory Recalls", "Upgrade Kit", "TPS Problems", "Paint Can Rattle", "Shifting (Transmission) Problems", "Lower Cam Chain Tension Adjuster" are all different search titles that will provide you with the sort of info you seek.
Up until quite recently, Triumph was honoring these factory engineering/faulty component issues via various "upgrade kits" and free service work, even for second owners and bikes well out of their warranty period. Apparently, that gravy train has seemed to come to an end.
I would not let such issues deter you from purchasing one of the older model Rockets. Just, do your due diligence, ask sellers the pertinent questions (regarding needed repairs, parts replacements and whether any "upgrade kit" work was necessary and/or done) and confirm that any such required work was performed by the seller's servicing Triumph dealership or otherwise.
In December of '09, I happened to have purchased an '07 Standard model that had about $5K in upgraded parts, accessories and bling on her. I confirmed with the seller and with his own, local dealership that my bike had had the full upgrade kit work performed. Consequently, she has provided me with over 10K miles of trouble free fun, other than for a faulty primary TPS that went south on me about 2k miles ago. Even for that failure on a bike nearly 18 mos. out of warranty and on its second owner (me), Triumph picked up the $109 cost of the part and I payed for the labor only!
My Mulberry Mistress came to me with 2700 mies on the clock, cost $10K and she's been worth every cent of that cost and more in miles and smiles provided.
Happy hunting!