From a story perspective, it makes absolute sense that he might have a thing or two to collect from Skyhold before he leaves for good. His most opportune time to do so would be after the party, when everyone is completely passed out. The Eluvian would be an easy in and out if necessary.
If not the above, then it is possible he did the painting before they left Skyhold -- confident in their success, he may have gotten ahead of himself.
I have to disagree that it makes absolute sense - it makes no sense at all, at least for me. It requires quite a few stretches to justify him returning to Skyhold, unnoticed and with enough time to paint something on top of it all: like assuming that absolutely everybody in Skyhold would be so wasted after post-battle party, that they wouldn't notice an elf who would require some sort of ladder or platform to draw a picture this big, even if he'd do it in record time. The empty space itself itself is at least 4-5 meters high and the picture is at least 2-3x4 meters, and its top reaches the wooden balcony on 1st floor. Even a Qunari would have a problem reaching and drawing anything beyond the paw and fallen Dragons' head.
It's just... bizarre.
And nobody notices anything missing from Skyhold, while the last sighting of him was from Leliana's people, who saw him shortly after the battle of Corypheus, heading West, while Skyhold is North from Temple Of Sacred Ashes.
2. Second - the last panel is not only sloppily drawn, it's sloppy in itself; drawn by someone with less talent or experience.
Well it is obviously a rough, and that's why I understand the state of it being sloppy. Your own roughs might be different in nature, but I for one have seen many people work from what looks like a complete mess in to something articulated and beautiful. When an artist is experienced, they give little worry about the look of a rough, so long as it reminds them of what their final intention is. And here, the final intention is visibly clear. So mission success, as far as roughs go. I understand you are referencing base artistic knowledge as your defense for this, like what seems to be a poorly laid out composition... but as we know nothing about Solas' process, then we can't say it is falling short. The intricity of the frescos come mostly from the use of contrast, pattern work and geometric power -- all things that wouldn't necessarily be present at this very rough stage. To me, I see the potential of it as it is now and I am fine with it.
Considering that we can't even agree whether the creature is a dragon or a wolf (or a hybrid of both?) or what the sword is or what the scene may depict it's hard to argue that intention was indeed clear.
And when artist is experienced, this is usually reflected even in their rough sketches. They may be a 'tangled mess', but usually there's enough confidence in lines and sense of proportion or composition to distinguish skill. In fact, one of the things that was drilled into me in my art schools is that sketches themselves reflect true skill of an artist and in fact that a good drawing starts from a good sketch first (especially in traditional arts, which are are far less forgiving than computer graphics). Personally, I find myself not in a place to disagree with that after years of experience (and that's coming from someone who thinks her sketches are pretty bad).
And we actually do know something of Solas' process - the codex in the rotunda explains that each panel is carefully planned before being drawn. It's therefore safe to assume then that even IF he began to draw on the plaster, he'd have it all thought out, maybe even had a variety of sketches or thumbnails on paper or vellum.
Also - the pattern work, the geometric power - even in rough form, this would be visible, considering the flow and composition of previous panels; especially considering that it's noted that Solas is a careful planner, whether in general, or when it comes to the mural. And pretty much nothing in the layout of the entire fresco or the last picture justifies its odd placement and prominent, horizontal line - in fact, it's even weirder that Solas would go for the effort to place the picture so high, considering that:
a. all other central figures are placed way lower, and start pretty much right next to ground
b. if he was already in a hurry, why would he made the task more difficult to himself, by placing it higher than he could reach it from the ground? Makes no sense whatsoever.
Now from a real world perspective, it is possible that the final panel was done by another artist on the team at Bioware (though I doubt it, to me is still looks done by the same artist). And as far as I am aware, Nick Thornborrow was responsible for the entirety of it (except for figuring out the logistics of sequence, I believe that was the brain child of other members of the team). More likely, in an attempt to make it look rough, Nick dumbed it down. Still supposed to have been done by Solas, though.
No, that's what we discuss about. From my perspective this picture was either drawn by someone else or dumbed down to a point that it's sticking like a sore thumb in terms of how starkly different it is compared to the rest.
There's a strong debate in the fan community as to if this is a wolf or a dragon, hehe. So you're not alone. If it is Fen'harel, it is possible he depicts himself as a combination of the two -- a wolfy looking dragon, not so dissimilar from how some people interpret the Behemoth. More likely it is representative of the Inquisition or Morrigan herself, though. The downturned sword could be the Inquisition slaying the foul beast, and the 'thing' watching it could be the greatest force of all three (symbolic of greater powers watching the battle). If it is in fact the dragon vs dragon battle, the larger one is symbolically the 'victor'. The one thing that I find curious is the ''drippings' roughed in. It could be mess from the wash, true... but it almost looks intentional. Here is a closeup of the panel in question:
Well then I definitely belong to the camp claiming that this is a dragon vs dragon, with victor being Mythal's guardian (basically a force allied with IQ) and a fallen one being Cory's "Archdemon", pinned to the ground by Inquisition's sword. Makes much more sense than the wolf-dragon hybrid, considering that it would be the only occurrence of such depiction of Fen'Harel in the game.
I think I've addressed this above -- but again, everyone is allowed their own interpretations and theories 
Furthermore, it has the same sense of 'flow' and works in with the rest of the paintings quite nicely, as you can see with a little rearranging.
We have to disagree with the work "flowing nicely" - for me, the image is annoying jarring in a sense that it doesn't fit at all in any conceivable way, aside from rudimentary connections between paintings... But I've already written a long comment where I pointed out numerous issues with it or the disrupted pattern and flow.
Solas would feel a guilt for leaving the Inquisition, it's not beyond reach to think he'd at least want to leave something behind. If it is a message of sorts, as people sometimes think, then this would be even more believable.
Why would he leave an ugly sketch with vague message though? He leaves in a hurry, his last words sounding like he quickly wants to assure befriended/romanced Inquisitor that he loved/respected them, because that's the last they'll ever see him (before he emerges as supposed enemy, I assume).
Prior to that, un-romanced, but befriended Inquisitor can tell in post-ToM scene that he sounds like he's leaving prior to battle. Solas then tells Inquisitor that he says his goodbyes now, because there may not be a later. Meaning he either wasn't sure he'll survive, or he may leave in a hurry anyway, saved orb or not.
....In fact, wouldn't it be even more hurtful, especially for romanced Lavellan (who can express her sadness to Leliana at Solas leaving without even saying goodbye) to know that he might've been in Skyhold, yet the only thing he left was a vague, sloppy mural, instead of heartfelt - even if impersonal - message of some sort that would feel way more significant?
I wholly agree. Though in my mind, he did it when everyone was passed out from the party... and also to collect a few of this things. xD
That we don't know of. In fact, the design notes on Soals' armors say that his outfits have been designed around the fact that Solas carries everything he has with himself, at all times - which is logical for a person who is used to fending for himself and actually it might not be the first time for him to disappear abruptly from someone's life. He probably has all the essentials and necessary things already packed, especially considering what I've said about goodbyes with befriended Inquisitors. He was very likely expecting to leave Inquisition, even prior to the battle.