Are all phenotypes normally distributed
Many phenotypes might be normally distributed assuming a large enough population size and many QTL (Quantitative Trait Loci) as the normal distribution is a simple result of the CTL (Central Limit Theorem). If it is unclear to you, you should definitely have a look at the central limit theorem.

Typically, if the number of loci is too low, the phenotype may for example follow some kind of continuous approximation to a Poisson distribution. Of course, if the allelic effects are correlated among loci or if there is some linkage disequilibrium or if the phenotype is bounded or discrete, or nominal, you may not end up with a normal distribution of phenotypes but all of that is a discussion for another time.


  I can't come up with any obvious example of phenotypes that don't follow a normal distribution


As, the second quote says, think of any phenotype that is discrete. Here are a few examples


sex
right / left handed
eye color


Now if you want a quantitative phenotype that is not normally distributed, then height (which is the bad example of your first quote) is very slightly bimodal due to an average height difference between male and females (look at Are males taller than females in humans?). You can also think of any phenotypes that are bounded. For example running speed. Athletes will cause a very long right tail, while people in wheel chairs will make a big stack of probability mass in 0 km/h.

There is a lot of things to consider when trying to guess whether a is normally distributed or not in a population. It will take some good knowledge of statistics and good knowledge of the genetics of the population.