The short answer is that it isn't practical to look at the waveforms directly...
The solution is to use some sort of spectrum based analysis...
(Which is basically what all modern test equipment, like our AP test sets, uses.)
There is almost no way to visualize the noise floor at -90 dB or so directly.
If you expand your sine wave as far as you can the amount of "fuzziness" dither adds to it just plain isn't visible on a screen.
In the old days it was widely said that "THD usually had to be over about 5% to be visible on a scope screen with a sine wave".
And, at the levels we're talking about, noise simply appears as a
very slightly less sharply focused line, at a much lower level.
And bear in mind that, with modern digital oscilloscopes, the signal you're looking at is being processed by an A/D converter...
And, unless you have a really expensive scope, the A/D converter that's providing the data for that display probably has
FEWER bits of resolution than your 16 bit CD anyway...
(They've traded resolution for the high sample rate that is normal on most oscilloscopes.)
The way we normally visualize that sort of thing is to use a spectrum analyzer or spectrum display.
If we feed in a test signal, we know what peaks should be present, and can analyze any extra stuff quite precisely.
Extra peaks at specific frequencies are generally harmonics (THD) or otherwise related noise (like IM products)...
And the "grass" between the peaks is your noise.
Specific "patterns" in the "grass" tell you specific things with great precision...
In general, when you add dither, you should see "smoother grass" because the purpose of the dither is "to eradicate any specific patterns".
In general, any noise that has any sort of pattern is annoying, while perceptually the "quietest and most innocuous noise" is pretty much random.
This all gets quite weird in terms of audibility...
We often see explanations of how, for example, "noise shaping" can be used "to push noise up out of the audible frequency range" on something like an SACD...
However, dithered signals often sound audibly quieter, even if the dither increases the noise
inside the audible range...
This happens because, even though it measures higher, the dither noise is
perceptually less annoying, so it is
perceived as "a lower noise floor".
One big catch is that this sort of analysis can only be done with known and basically static test signals.
For example it would be difficult to do with music... because that spectrum display would vary wildly... and no two samples would ever be the same.
(So you would be unable to average a whole bunch of measurements... which is one reason why spectrum analysis is able to offer us detailed results.)
This makes it very difficult to test for things like "signal correlated noise" (distortion that appears "in time to the music".)
Luckily, since this is difficult to measure, there are ways to design so as to avoid the risk that it will occur, and it usually isn't a problem these days.
A really good analogy for dither is one of those wave machines that were quite popular some time ago...
The goal is to prevent specific small noises from being annoying or obtrusive...
And the solution is to replace them with a slightly higher level of innocuous noise...
(In crude terms: "It drowns out the annoying noises with slightly louder, but far less annoying, noise.")
And this is precisely what dither does.
Also, incidentally, as this pertains to analog recordings...
One of the reasons dither is generally not added to analog recordings to improve the way they sound is that virtually all analog sources
already contain dither...
Tape hiss, hiss from your microphone preamp, and the steady hiss from the surface of vinyl, all qualify as "naturally occurring dither"...
To answer your question, however, unlike distortion, there is no way to "null out" noise, because it is random (so it "doesn't" ever cancel).
This makes it difficult to compare the noise between two signals directly.
So the only way to compare an analog signal directly to the output of some digital process that was reproducing it would be to digitize both of them so their spectra could be displayed and analyzed.
However, another option would be to null them, and analyze the result...
If you null them, and the result you get sounds like pure white noise, or with no detectable pattern...
Then you can infer that the differences between them are probably also the result of random noise...
And you can then digitize and analyze that difference signal, and perform a spectrum analysis on it, to confirm that the differences are random.
(This is basically how something like the AP works... you feed in a test signal, look at the output, ignore the test signal, and analyze what's left over.)
Unfortunately there is a "catch" there as well...
Something like a slight change in frequency response, even though it is audibly harmless, will prevent you from attaining a reasonable null.
So what you'll be looking for in your null is "an audible difference that sounds like the music and lacks any obvious and annoying artifacts".
(To offer an easy example... if all you hear in your null is a "spfut" noise on every drumbeat, then something is probably clipping the drumbeats.)
If I really wanted to be smarmy I would point out that... on that picture... of "the nice smooth analog waveform"...
The "smooth analog waveform" in the picture is actually made up of little rectangular pixels ( "digital stairsteps")...
And your monitor doesn't even include a reconstruction filter to turn them back into a real analog image...
(So, in other words, their "picture of the ideal analog waveform" is really just a picture of a digital waveform with smaller steps.)
Isn't that interesting...
Okay! But! Same image pixelization for the screwy digital images. Display resolution not withstanding .... is there a way to look at an actual comparison of what an analog wave looks like, and then on the same device what the wave looks like after A/D/A at say 96/24? Of course there is, but nobody does that ... they use the drawing. Because the scope waves would be indistinguishable. How about without the dithering though ... is there a way to see that? Would it look like a noisy sine wave?
