Just take a look [...] and check what your eyes tell you :-)

This is the same procedure that leads a lot of people to lose a lot of money trying to pick stocks, and a lot of other people to believe in the efficacy of prayer. Human eyes attached to human brains are very good at seeing patterns that aren't really there.

I am not a climate scientist and haven't looked at the data in detail. But, for what it's worth, when I eyeball the plots what I see is a highly noisy time series whose last 10 years or so do indeed look cooler than trend but not so much so that I'd want to rule out random variation as a sufficient explanation. And at least some people who have looked at the data in detail have arrived at the same conclusion; see e.g. passive_fist's second and third links.

I don't know whether those people are right, but what they say seems to me obviously credible enough that saying "just eyeball the data, it's obvious" is really bad advice.

[EDITED to add:] Maybe what's actually going here is different interpretations of "the hiatus exists". It seems fairly uncontroversial that (e.g.) the slope of the least-squares straight line fit to mean surface temperature from 1998 to 2013 is somewhat smaller than that of a corresponding fit from 1983 to 1998. (Though IIUC this is in fact what the NOAA guys are calling into question.) On the other hand, it's obvious from, er, eyeballing the data that whatever medium-to-long-term trends there may be are overlaid with a lot of short-term variation, and the question is: does that fact about slopes of 15-year fits actually give us reason to think that whatever processes are responsible for the longer-term increase in measured temperatures have stopped or slowed or otherwise changed? The answer to that could well be negative, and my own impression on eyeballing the data is that it probably is negative, and that's what I mean by saying it's doubtful whether there has actually been a hiatus.