The evidence for this planet is found in a clustering of the perihelion positions of the six most distant solar system objects in a particular direction on the sky, and the hypothesis is that they are counterbalanced by a massive planet whose perihelion position lies in the opposite direction. However this direction not very well constrained, and as far as I can see there is no evidence as to where this planet might be on this supposed orbit. So when they say they have a vague idea of where it might be, they do mean vague, and it could be anywhere in about half of the sky. Large telescopes have small fields of view, even survey telescopes which are designed for searches have a field of view of about 40 square degrees. Thats about one thousandth of the area of the sky.
There are some smaller facilities with fisheye lenses and things which can survey the bright stars in the sky over a wider area. So lets work out how bright this thing will be.
Lets assume it is like Neptune in terms of size and albedo (the fraction of light it reflects). Planets are only seen in reflected sunlight, they do not shine by themselves. It seems from the paper that the distance from the sun is likely to be about 10 times that of Neptune but its also 10 times as far from us as Neptune. And inverse square law being what it is, that means its a factor of 10 to the power 4, or 10,000, fainter than Neptune.
Astronomers work in magnitudes, Neptune is an 8th magnitude object (not quite visible to the naked eye), this new planet will be 18th magnitude.
This is well within the capability of even modest sized survey telescopes, but not one of these fisheye lens things. The main reason being that there are loads and loads of stars in the sky of this magnitude. Technically the fisheye things will be confusion limited.
Also, how do you know that you have seen it? You have to see it move is how, but it moves pretty slowly, it will be moving at a hundredth of the apparent rate of motion of Neptune (a factor of 10 because of Kepler's laws, and another factor 10 because of projection). So you have to look at the same patch of sky repeatedly for things that move very slowly.
If it exists the Large Synoptic Survey Telescope
will be the thing to find it, but thats not ready yet.
But I have my doubts. Six is not a huge number of orbits to base such a supposition on, and the probability they work out for this alignment to happen by chance is not very meaningful because they are working it out for a configuration that they have already observed (a posteriori statistics). I wonder whether Dr. Mike Brown, well known demoter of Pluto, has a funding review due.