Sure. Why not? I guess it depends on your goal. For global behaviour of a differential equation, increasing the number of points and resolution may not add so much additional benefit - it may even have the opposite effect of increasing clutter.
The one I have drawn in this post is borderline in my opinion. I could have made the little slope lines a bit bigger and used 1/2 the amount of points, and the slope field (aka direction field) would have told the same story.
However, if you want to zoom in on a behaviour near a critical point, you may want to increase the resolution to accurately depict what's going on.
To expand on the answer a bit. So for 2-dimensional first order ODEs there is the Poincaré–Bendixson theorem. This tells you all the possible types of solutions that can occur. Using this and studying the vector field it is easy to prove which solutions occur.
In the case of equilibria (for n-dimensional ODEs) you have the Stable Unstable and Center Manifold Theorem. These theorems tell you what happens close to an equilibrium.