Other than wearing out a set of brifters, my Ultegra triples have been completely trouble free. Of course, I replace my own cables and housing and adjust them myself. It's easy to do it wrong, but worth learning to do it right. Just follow the package directions. In the back, it depends on your strength and terrain. I used to run a 25 in the back until I got old and wimpy and went to a 27. For long 18% pass climbs it'd be worth having a 34.
Although it's possible to break an Ultegra brifter by shifting both handles really hard, especially with heavy gloves, so you do have to be careful of that.
What goes wrong IME is headsets, wheels, and tires. CK headset and building your own wheels goes a long way to help. Also cables breaking, so a spare cable is nice. But if you break a rear cable, at least with a triple you still have a 3-speed bike.