The 2011-14 "Coyote" powered Mustang GT and even the Boss302 are some of the best bargains out there right now for a fun, V8 powered, low cost, track worthy car. They do, like all cars, have some issues that will be outlined in the upcoming "Mustang Buyers Guide" that J.A. referenced.
All of these issues easily fixed or upgraded, and all things that virtually any modern car has to deal with - lack of camber, soft springs, and "too much altitude". 
(would you believe the car shown above is the same car below?) The article will show more of this, but here's a few quick observations...
Having owned several of these "late" S197 V8 Mustangs, as owner of a shop that's worked on 50+, having developed and sold suspension and brake parts to 1000s, and having driven and/or coached right seat in 80+ of these, I've perhaps got a unique perspective. First hand knowledge of these cars run in competition within Solo, Time Trial, W2W, and more. We have explored the upgrade paths, found the weak links, developed parts to fix the worst bits, and have been witness to many hundreds of terrible products pushed to this community.
Many of the issues I've seen pointed out in this thread already come from a common source - driver induced. The "terrible" clutch that these cars have? It's actually fine if you aren't a speed shifting lunatic drag racer. My wife and I both drove this 2011 GT above at NASA weekends, often back-to-back in different run groups, for 20K miles on track over 5 years.
We also drag raced it, autocrossed it, and very rarely street drove it. We never had a clutch failure, missed shift, or other issue that could be clutch related. I wouldn't say that the clutch is "over-built", but it is adequate for the power the car made (447 whp with headers, a cold air & tune, on 93 octane).
We had zero issues with the engine but we also didn't over-rev the engine like many - peak power was at 6400 rpm, so we changed gear at 7000, and never exceeded that. These DOHC V8s have about 40 feet worth of heaving timing chains, which then has a lot of MASS. When you rev these to 8000 rpm and beyond they start to eat the chain guides, oil pumps shatter, and all sorts of bad things happen. As backwards as this sounds, these DOHC V8s do NOT like the higher RPM ranges that people associate with them.
But I've ridden with some real ham fisted gorillas that felt that since this car came with a 420+ hp engine that therefore the transmisson and clutch should be INDESTRUCTIBLE. That of course is not the case. I've had to tell HPDE students to CHILL OUT with the massively over-done shifting, clutch abuse, and USING THE SHIFTER AS A HANDLE. If I had a dollar for every time I've had to gentle tap a driver's hand who was holding on for dear life to the 6-speed shift knob, I'd be a thousandaire.
Leaning on and abusing the shifter seems harmless, but it bends shift forks, and that leads to these "long engagement" and delayed shift issues. The Getrag MT-82 6 speed in these 2011-14 GT and Boss cars is likely the weakest part of the entire chassis, too (we had one that failed, in gear, at 18,000 track miles - it was from heat, not missed shifts). "Some drivers" can kill these transmissions multiple times under their ownership, while curiously others don't seem to have these problems - even fast drivers. Some people can also break an anvil with a feather, and the "typical Mustang crowd" is chock full of this lot! 
#BlameTheVictim
Now to address the OPs question - should he buy a high mileage Boss 302? Sure, if the price is right. But remember, the "Roadrunner" engine in the Boss isn't really all that special, and what makes the "Boss" difference is mostly the intake manifold, the Brembo brakes (optional on the GT since 2011), a Torsen differential (optional on the 2013-14 Track Pack GT) and a diff cover (also on the Track Pack). They also come with the Recaro seats (very nice, and optional in other cars), and some subtle aero treatments. And a lot of stickers. The main convenience is - this one is easier to spot among the used car offerings, as the Track Pack (which has almost all of the same features) is not noticeably marked as such.
The miles don't really "hurt" these cars, but inattentive and abusive owners do. It is usually easy to see the abuse before you buy - look for balled up rubber in the rear wheel wells (drag racers), or excessive "power mods" underhood. If they have maintenance records and you see multiple transmission or engine replacements, that is not a GOOD thing, either.
Also, don't get hung up on the Boss302 thing - there isn't really a big enough difference to the 2013-14 Track Pack GT (above) to make them have enough "prominence" to fetch a premium price anymore. This model is very different than say... the S550 chassis Mustang Shelby GT350, which did come with some rather unique items, a unique engine, unique brakes, wider wheels, differential coolers, etc (caveat: the 2022-23 Mach I had almost all of that without the vibration prone flat plane crank "voodoo" engine that had lots of failures). So if you can find a Track Pack car, or even a 2011-14 "Brembo" optioned GT 6-speed manual, and it isn't heavily modified, go for it. My racing buddy has a 2011 GT Brembo car with 127K miles and it runs great to this day, and he's had it since new - the only thing he has had to replace are tires and brake pads.
The S197 has absolutely AMAZING and fast acting ABS programming, which is the envy of other car makers this side of Porsche. We swap the S197 ABS onto lots of other chassis because it is SO GOOD. To make up for the weight, you have to keep the "tire width-to-weight ratio" in mind, All of the images shown here are cars we have upgraded with 11" wide wheels and 315mm tires, at the minimum.
Not everyone likes driving a RWD car with more than 400 hp, and I get that. But if you get bored with an 86 or Miata and want "that other vector" to challenge you (ie: forward acceleration), these can be great candidates for a track toy for well under $20K these days. With these 2011-14 V8 Mustangs you get amazing power, reliability (without gorillas shifting them), great brakes (for the time), amazing ABS, and with a few dollars spent - pretty decent handling. Again - you can never have too much wheel and tire width on heavy, powerful pony cars. The car above is on 335mm front and 345mm rears with 18x14" wheels. If they made a wider tire, we'd use it! 
The only option in the Mustang world that is better is... the next generation. The S550 chassis has an updated double-ball jointed front suspension, even bigger/better brakes, and an amazing independent rear suspension. The basic V8 S550 GT gained no weight over the outgoing S197 chassis' GT version, but the handling and ride are better. They are newer, hence more money now...
Cheers!
