Check the Issues/Warranty/Recall subforum:
http://www.ft86club.com/forums/forumdisplay.php?f=72
There have been two confirmed issues that could affect an FRS/BRZ/86 that would require major rework.
1. Check Engine Light/Slip Light error which never got a real solid answer seems to be eliminated. This resulted in a couple blown motors, a couple replacements and a couple of services requiring replacement of camshaft/timing equipment/ecu replacement. Again this seems to have been "solved".
2. Injector seals blowing out, current root cause is said to be shifting at or near redline and when you step back on the gas the engine will knock, over time this will degrade the seals until they no longer seal the combustion chamber causing a lean condition, more knock and eventually things break. The fix should be an ECU update to fix the transient timing tables to prevent the knock under hard acceleration, but there is concern that it may be caused just by heat buildup, in which case a new seal design will have to be released or they will have to find a way to keep the engine cool (lol). If you avoid hard shifting at redline (or at least are easy getting back on the gas after a shift) there shouldn't be any major issues.
Everything else is small or a one in a couple thousand fluke.
But like everyone else here I'll post anecdotal evidence: 10k miles, zero issues.