After doing my reread of the series and thinking about it as a movie, I feel like it would be really tough to adapt. And not because of the sexual violence or anything (to be fair, a lot of that could be implied rather than directly shown, which is often a lot more effective anyway). Even with an infinite budget, I just think it would be damn hard to do without being able to see into the character's minds -- especially Kellhus, and to a lesser extent, Cnaiur. It would almost have to have flashbacks, both to the time of Moe and Cnaiur, and possibly flashbacks (some of which would likely have to be brand new) to Kellhus's time in Ishual, which would serve as explanations of his Dunyain powers. Obviously some information that could be cleverly delivered in other ways, but there's just a shitload of backstory to the Cnaiur/Moe/Kellhus storyline that is taken almost entirely from internal thoughts, and it would be hard to reconfigure all the necessary stuff into action/dialogue.
That is, unless, you did voice overs. And that's...risky, especially in something like an epic fantasy. You could go for something along the lines of Terrence Malick's Thin Red Line, which might work if properly executed (and could be damn interesting as well). Or, you could have some kind of narrator, in the vein of The Assassination of Jesse James by the Coward Robert Ford. Both options could work, and both could potentially be really great (or turn out horrible). Overall though, I think a TV show would probably be the best route. It would of course allow a lot more time to get all the important details in (I think any film version would almost certainly start collapsing multiple books into a movie; there's just too many books), and if it was on something like HBO, then really the violence, sex, and violent sex could be worked around, especially considering some of the over-the-top shit you see in True Blood and Game of Thrones. The Sranc are often mentioned as a big issue, but I think that could be dodged with some good exposition and powerful (but subtle) imagery. Clearly it would be a challenge in certain cases, but not the main impediment in my mind.
The only major drawback for the TV show route is the budget, which would be substantial considering the sheer scale of the thing. I mean look at how expensive GoT is, and that story, relatively speaking, is a lot more grounded in reality. TSA is loaded with crazy depictions of magic, several types of inhuman creatures, ridiculously huge war scenes, etc., not to mention basically every other cost that goes along with this type of fantasy (costumes, sets, make-up, etc.). That being said, CGI and special effects in general become cheaper as time goes on. Something on the scale of GoT (especially season two and three) ten years ago would be virtually unthinkable. So, maybe ten or fifteen years from now, I could see TSA being feasible for a cable network like HBO -- and honestly, where else would something like this be made? The bigger problem in that case (and probably the biggest problem overall) is that TSA is not the most popular series. I mean it's obviously on the upper scale of fantasy lit., but it's still a pretty tough sell to a casual audience. That being said, I do think the series will gain popularity in the future. It just smacks as one of those works that will take time for people at large to fully appreciate the strengths of.
ETA: Although, as others have mentioned, perhaps the best road to take is animation. Almost every issue is solved, really, and with the right style and talent, it could be damn amazing. Unfortunately the West is a bit slower than the East in realizing that animation doesn't have to be exclusively relegated to the realm of children's cartoons or comedy.
