My hand shook and the photo came out blurry.
When taking night shots, be careful of camera shake.
This camera has excellent image stabilization.
There is a deviation in the measured values.
His opinions are always consistent (without deviation).
This camera has a feature that corrects for camera shake.
There's no inconsistency in what he says.
ブレ and 触れ sound almost identical, but 触れ means 'touch/contact' while ブレ refers to blur or deviation, so they are unrelated in meaning.
Katakana spelling is common for this loanword-derived noun.
Hiragana spelling is also used, especially in casual writing.
The noun form of ぶれる, “to shake, blur, or deviate,” conventionally written in katakana in technical and colloquial use.