I was on my phone before, now I can type a bit more…
There were indeed some early flaws that were fixed after the first few years. Some of the bikes that had problems were improved by installing what they called the Update Kit. Among other things it included a new cam chain sprocket and sprocket key, updated 2nd gear and a couple other transmission parts, and a few other items. If you were looking at old models, you could get the VIN and check with a dealer if the kit was ever installed.
But again, many people have ridden tens of thousands of miles on the old bikes without the kit installed. That said, why take the risk if you're not eager to tear into the engine if something breaks. 2010+ is no guarantee of a problem-free bike, but at least you're avoiding known early flaws. Then again, if your budget was only $4k, buy an early model and ride the hell out of it until something breaks, which may never happen! There are just a lot of variables depending on what you want.
As far as what to look for when buying used… I just don't know if I have a very good answer. Others may come along with better specifics, and for sure the more searching and reading you do on the forum before buying, the better educated you'll be. But when I think about what I would look for if I were checking another Rocket to buy right now… other than the obvious of checking for leaks not just underneath but all around, including the final drive/bevel box… it's difficult to say if you don't already know the R3's. They tend to make strange sounds and shift with a clunk. There have been many discussions over the years of people worried about a sound or feel and everyone else replies… that's normal.
So, short of having a dealer check it out or getting someone from the forum who lives nearby to take a look… I think you really just go with appearance, VIN history from a dealer, any maintenance records, and the vibe you get from the seller. It's like buying a used house. If you check out the basics you won't go too far wrong and will have something workable, but you'll be finding clues and quirks about its past for as long as you own it.
Also if you haven't, take a look at the forum classifieds. I can think of a handful of bikes for sale right now from experienced forum members, in a range of years and prices.