The camera position is not the only thing that is interpolated. The camera focal point (where it is looking) is also interpolated along another spline. You may have to edit that one too.
That’s very sad. Because when I save camera in the timeline, I expect everything to be saved about it.
And in the view-port, it appears like this. But in rendering, it is not. 
then double click on the Path… in the Camera Values column, you can edit both the position and focal point control points.
Of course. And I save these as I see them in the viewport. End the configuration is reproduced when the field is called in the editor. But during rendering, camera misses these values; going somewhere else by “inertion”.
I’m not sure… it shouldn’t be.
But it really looks like this. I would say, if the viewport can be 3-point interpolation, the rendering looks like an approximation with the polynomial of 5th order, that “oscillates” +/- Infinity between points on sharp turns.
BTW, Since you mentioned the focal point, I have to say that the mouse control is very hard to use, because it neither controls the distance to focal point not position of that point. And the focal point itself is not obvious.
Only FOV seems to be controlled, but called “ZOOM”, which brings more confusion. ZOOM is neither FOV, nor distance, but just a 2D enhancement of image; not very applicable to 3D editing.
In result, it is very hard to control camera.
Why don’t the dev. team look at the experience of other 3D software, starting from 3Dstudio, till modern products? Talking about simplicity, the simplest 3D control I ever seen was in HFSS editor. And it never failed. Some software offers adaptive focal/rotational point, locking on objects, or at the average distance of the swarm. And mouse rotation is usually made by the intuitive model of the “crystall ball”; reacting according to the side you “touch” with the mouse.
But in Paraview I can not intuitively understand where is the rotation vertex/focus, where should I move mouse to rotate in particular direction.
but rotated strangely about the axis it is looking along if your path triggers the corner case.
Do you mean roll? well, it is common, and at least natural, like the Berry phase. (consider rolling along the surface, defined by camera position and focal point trajectories) slowly rolling away because of coordinate transformations is one thing, but loosing this “surface” is very different.