There are still applications where e.g. random forests beat the crap out of all kinds of deep learning algorithms in (a) training time (b) predictive quality (c) prediction time.
We should stop hyping this. I am a researcher working in deep learning myself, but the current deep learning hype is actually what makes me worry that I will have trouble getting a job because industry will be disappointed a third time.
Still, deep learning has done nothing more than classification right now.
What about predictive distributions, regression of complicated outputs (e.g. periodic data) and, most of all, heterogenous inputs? Right: nothing impressive has been done in that area, despite of huge amounts of practical problems.
Let's see if deep learning generalizes to those things. If it does (and I personally believe so) let's be happy. Before that, we still have to envy what Gaussian processes, Gradient boosting machines and random forests can do what DL so far cannot.
http://homepages.inf.ed.ac.uk/imurray2/pub/12deepai/ has predictive distributions from deep learning, passed on to time-series smoothing for articulatory inversion. It's a previous neural net approach made deep, and working better as a result.
(I agree that like any machine learning framework, neural networks have their strengths and weaknesses, and open challenges.)
My point is (I did not really write that above) that deep learning does not stand unchallenged in this domain. Its dominance is so far "only" apparent in vision and audio classification tasks.