With respect to deep learning, most of the work I see involves pulling existing networks off of the Caffe Zoo and retraining them with proprietary datasets or fiddling with Theano to reproduce the works of others. These efforts mostly end in failure, usually after a blind hyperparameter search.
The easiest way to separate the winners from the losers in deep learning and elsewhere is to ask them to derive the method they are using and explain what it's doing. For the most part, I find the above people are incapable of doing so for backpropagation. Bonus points if they can write (relatively) efficient C++/CUDA code to implement backpropagation from the ground up.
Edit the above paragraph for PCA, ICA, GP, GMM, random forests or any other technology/algorithm. If one has a decent grasp of the underlying logic, the instincts for adapting it to new domains/datasets come at no additional charge.