A tuner accuracy is +/- 0.5 cent means that it is highly sensitive or just decently sensitive for pitch accuracy?
According to Wiki., a one cent change is imperceptible to most humans, so half of that is going to be a pretty accurate parameter change. One semitone (say from E to F, or A to Bb) is easily recognised, but when that interval of a minor second is split into 100 different 'notes', most wouldn't spot note 77 from 78 as being different/out of tune. Halve that difference, and I'd say it's certainly accurate enough for me! Just how much more accurate would one need it to be?
It depends on for what purpose. For tuning a violin or guitar, you should be fine. For tuning a rigid-pitch instrument with composite notes (like an accordion or organ) tuning two notes independently with 0.5 cent error each that are supposed to be sounding in unison (either with the same frequency or a fixed ratio like 2:1 or even the 3:2 of an organ's quint registers) is not going to sound well.