While it's a good idea to check visually whether your intuition matches the result of some test, you cannot expect this to be easy every time. If the people trying to detect the Higgs Boson would only trust their results if they could visually assess them, they would need a very sharp eye.
Especially with big datasets (and thus, typically with increasing power), statistics tend to pick up the smallest of differences, even when they are hardly discernable with the naked eye.
That being said: for normality, your QQ-plot should show a straight line: I would say it does not. There are clear bends in the tails, and even near the middle there is some commotion. Visually, I still might be willing to say (depending on the goal of checking normality) this data is "reasonably" normal, though.
Note however: for most purposes where you want to check normality, you only need normality of the means instead of normality of the observations, so the central limit theorem may be enough to rescue you. In addition: while normality is often an assumption that you need to check "officially", many tests have been shown to be pretty insensitive to having this assumption not fulfilled.