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It depends which software you're talking about.

I've found that you have to go around objects which, in a lot of cases, means you have to wait for the current view to finish rendering in order to know what's what and even then, I have a problem clearing low-hanging objects.  My biggest problem there is underlighting that particular area and not seeing something, then rendering the anim and ... oops...  I will say that in the case of the Mandelbox, it's pretty slick to have the camera go through things, as it does the nifty cut-away thing, but the Bulb doesn't seem to like to do that as well, and does end you up with brown or similar chunks of unattractive innards.

As far as conceptualization, in my case, I tend to draw on my 3D experience where I pretty much had to learn to avoid all things solid -- which in the case of the Mandelbulb isn't easy especially with some of the deeper zooms where discerning depth is a challenge.  In the navigator tool, I spend a bit of time backing out of places where I seem to have wandered inside something solid without meaning to. 

I tend to agree with you about the convenience of cameras in 3D tools, esp LightWave or 3DSMax (haven't used Maya and TruSpace's camera was a bit cumbersome) where you have, basically, an external view and can adjust the camera both from it's own viewpoint, but also from various viewports.  I'm not sure how practical (or difficult) it would be to have something like that, here, where you'd have a wireframe representation of the solids in the Mandelbulb object(s) and the ability to put in a splined path for the camera.

I guess to actually address your question, the camera has to be moved around objects, using 'rotate' to bank around outcroppings and 'look' to point where you will end up with the 'walk' functions.  My biggest challenge with this is being able to point the camera actually towards the particular location to which I wish to zoom. In the darker recesses, I tend to have to do a lot of 'sliding'/'looking' to get aimed properly.

Please read also the textfile in the M3D archive, there should be some basic
explanations about navigating...

The buttons on the bottom of the main window are not designed for fly-throughs,
use the navigator instead.  Then you should not have troubles with flying through
the bulbs.  Rendering time depends much on the "Far plane" value, decrease it for
speeding it up with loss of far background structures.

The marquee zooms into the Zmid plane, regardless if there is an object or not,
so you can end up in the bulb.  That is more for 2D navigating.

M3D differs in many points from the common navigation, that's true because it
uses (still) a viewplane instead of a camera point.

Duh - my apologies, I was just going through the recent new posts and forgot to check the particular forum location before posting my reply !