Is it bad to water plants after the sun has gone down or near dusk? If so, why?
An advantage is that you can conserve water because of less evaporation -- there's no sunshine.
A major disadvantage is the flip side: the sunshine can't help dry out plant leaves that get wet. Some plants don't like cold and wet foliage. These conditions can foster blight on tomatoes for example. See also this answer that mentions being careful not to leave basil damp overnight.
So if you're watering in the evening, don't spray the foliage. Use a soaker hose or other irrigation technique that targets the roots instead of the foliage.
Early morning is a good time to water. You can give the soil a good soaking and everything has a chance to penetrate before being burned off by the sun. Anything that gets on the foliage will dry up with the sun and you're less prone to disease and fungi.
If anything, the opposite is true. There are two reasons:
First is evaporation. During the day it is hot and the water evaporates quickly - i.e. it is effectively wasted. This is why cities and water authorities have recommendations, regulations, and by-laws controlling when you can use landscape irrigation systems.
Secondly, water on plants in the sun can cause scorching - regardless of your latitude. This is because the water droplets act like small lenses, concentrating the sun. So you really want the water to be off the plants when the sun is out. This usually makes the evening at sunset (or after) more favorable to early morning watering. Of course drip irrigation is another way of avoiding this problem.
It is true that watering when the sun is out can cause scorching; on the other hand, although evening watering reduces evaporation, it leaves plants and the surrounding soil wet, or at least damp, at nightfall; besides providing fertile ground for diseases, this attracts more pests, particularly *slugs.*
This link favours watering in the morning and, if that's not possible, then late afternoon (with enough time for the plant to dry out a little).
The dangers associated with scorching (daytime watering), are far outweighed by the problems associated with damp sulky plants (nighttime watering).
It is only better to water in the evening or early morning from a conservation perspective due to evaporation of this precious resource.
Otherwise, the idea it's bad to be watered under the bright midday sun because it hurts the plants themselves appears to be a myth. See this article by a well qualified horticulturist debunk it.
There are many causes of leaf scorch, but irrigation with fresh water is certainly not one of them. Hundreds of scientific publications on crop plants, turf, woody shrubs and trees have examined foliar scorch, and not one of them has implicated midday irrigation as a causal agent. What does cause damage, however, is suboptimal plant-water relations, which can result in tip and marginal leaf scorch, shoot dieback, stunted growth, and leaf abscission.