Would anyone care to post any dissonant scales, or direct me to a site providing them?

And, hypothetically, could you construct an entire song that is dissonant?

No such thing as a dissonant scale. Dissonance applies to harmony: notes sounded at the same time. You can get dissonant harmony from any scale.
Or you can simply add chromatic notes to any scale to give you more dissonant chord options.
Sure. Listen to Stravinsky...

Dissonance is a cultural thing. It derives partly from physical factors in sound, but only has meaning within our musical culture of harmony.
In most popular music (including jazz and rock) dissonance (complex frequency relationships) is used as a contrast with consonance (simple frequency relationships). Songs begin and end consonant (normally), but go through dissonance (to varying degrees) in the middle.
IOW, it's the movements from consonance to dissonance and back that make sense of the whole thing. It's what a chord "progression" means: chords only "progress" (have a sense of forward movement) if they use dissonance in a certain way, that leads us to expect (through our familiarity with the style) a tendency towards "resolution", or more consonant harmony.

But modal jazz (eg) can be dissonant with no sense of forward momentum. E.g., a phrygian modal chord (susb9, 1-4-5-b7-b9) is dissonant, but the dissonance is a stable sonority (a nice sound in its own right), not one that needs to "resolve" anywhere.
Even so, it still depends on a familiarity with the style (the rules of the genre) to appreciate it.

It does depend on who your audience is. A pop or average mainstream rock audience will be bewildered by sustained dissonance with no direction or resolution - "what's all that noise about?" . (This is the same kind of response as when people look at an abstract painting and say "what's that supposed to be?" IOW, they expect a clear meaning, certain rules to be followed.)
A modern jazz audience, or heavy metal audience, may be more receptive - although a jazz audience might except some kind of formal content, hints of jazz awareness, and certainly a good deal of improvisation.
IOW, dissonance (for its own sake) is a fringe interest.
There is a lot of music around (although largely "underground") which you might characterise as "dissonant", but its practitioners may not think in those terms. Eg, in free jazz, they're more interested in sound itself, the various unorthodox noises instruments can make, and the conversations you can have with them, than in harmonic concepts such as dissonance. IOW, dissonance is a by-product of the music, rather than an intentional content.
That would be the case in a lot of 20th century "classical" music as well. They've gone beyond out-dated concepts such as "dissonance" and "consonance" - which would be considered part of pre-20th century "functional" harmony (the kind of harmony still widespread in popular music of all kinds). That music sounds "noisy" or "dissonant" to the uneducated audience - for whom "noise" (in particular) is a "bad thing" .

You can have quite unpleasant sounding scales, but not really any dissonant ones. Dissonance is generally referring to wrong notes or intervals really.

A good 'unpleasant' scale is, of course, the chromatic scale, as well as teh Nonatonic. Persian is also quite weird, as are the symmetric Octatonic and Hexatonics. Wholetone is also weird, because as you begin to ascend it, it sounds major, but then these odd intervals start creeping in. It's good for neurotic music.

I guess on it being really about wrong chords, then in scale-kind-of format, dissonance could apply to arpeggios.

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