First three episodes aside, this season can be described in one word: Disappointing.
I highly suggest reading the manga of this arc (the first three episodes aren't in the manga but instead have a light novel as the source material; starting from episode 4 is where the manga picks it up), because it's much better. That would be chapters 38 - 52.
Story
There are two major arcs (with a few "fillers" in between; I put that in quotes because though they seem to be fillers, they were still in the manga).
The first arc was probably the best this season had to offer, and spanned episodes 1-3. It revolved around mostly Chuuya as he searches for his relation to a creature of chaos/destruction which leads him to running into Dazai and the mafia, and is the story of how he joins the Port Mafia.
This was the best arc out of all of them, a solid 10/10.
The next episode is a prelude to the House of Rats arc (the major "arc" of the season), and then it goes into what seem to be filler of wrap-ups after the incident with the Guild. We see what Fitzgerald is up to, and there is an episode involving Kyouka and Demon Snow...as well as Atsushi and the Headmaster in that same episode. These "fillers" (again, they were in the manga, so not really fillers) between episode 4 and episode 8 (where the House of Rats arc really starts) are rushed and though were fun to watch, were severely lacking to their manga counterparts.
This section/arc earns a 3/10
The next set is the major arc of the season, the House of Rats arc which spans episodes 8-12. Fyodor, the "demon", is on the move to attempt to obtain the book for his own purposes. Since he doesn't have the resources like Fitzgerald did to try and destroy the city entirely, he uses his cunning mind which is on par with Dazai's own and pits the Port Mafia against the Armed Detective Agency.
Would have loved to give this a higher rating, but it was rushed and the final episode has many issues...so, sadly, I have to give the anime version of the House of Rats a 6/10 (and that's being generous). I'd give the manga a near perfect score.
Characters are the same as the ones from previous seasons, with the addition of new antagonists...so, I'm not going to give it its own section like I normally do
Sound and Animation
The opening and ending songs are brilliant, and again keep in tone with the feel of Bungou and the past two seasons of OPs and EDs. Not as fond of the arrangement in the visuals during the ending song, but it's not that bad. The OP and ED songs are what save the "sound" score...and the voice acting which was excellent as usual.
What kills the sound rating is the final episode, which has music in the background throughout nearly the entire episode, and much of the music doesn't match what's happening or the high-stakes incident on the screen. There were dozens of times when the music was too loud compared to the characters talking, and detracted from scenes which should have been much more impactful than they wound up being.
So, of course, major minus points for that. There were even a couple of times when the downward, thin-faced angle wasn't appropriate.
The animation all season has been weird. New angles are used (bug eyes and thin faces) to emphasize an eerie moment of a character just being creepy (or highly determined, in some cases). It certainly does accomplish the goal of emphasizing the emotion, but it's used so often that it just feels uncomfortable. Some of the character designs seem thinner than before, and the line thickness can't seem to stabilize. I believe prior seasons often had thicker lines for more comedic scenes, but this season couldn't seem to get that done properly and had a mis-match of line thickness.
Overall
The House of Rats was my favorite arc in the manga, and they blew it.
Things such as Kyoka's relation with Demon Snow and the chapter/half episode of Portrait of a Father were rushed to the point where the viewer can't even empathize with the character.
When I read Portrait of a Father for the first time in the manga, it actually hurt; I cried...and was horrified in all the right places. When the episode came out, it did things so wrong that I felt nothing.
If done properly, anime can make me cry even if I know what's coming due to the manga. BSD failed to contain any sort of emotional impact past episode 3.
Everything was so rushed...scenes were neglected, and even some explanations were neglected in favor of smushing it all together to cram 7 chapters with about 30 pages each (the House of Rats arc) into the span of episodes 8-12.
The ideas covered in this season (with the exception of episodes 1-3 which again, never made it to the manga from the light novel) spans chapters 38 - 52. All within episodes 4-12.
Oftentimes, there are scenes cut from the anime which were in a manga, but this time there were some more crucial things cut (one which was briefly touched upon in the final episode near the end). Then, of course, was the mess of a final episode.
Of all the complaints of "rush job" I have for this anime, the last episode is the worst offender in how rushed it was, barely being able to hear the characters talk over the music, and one scene where it would have had a much greater impact if they had at least silenced the music for the duration of the talking.
This season was just a mess. It started out strong, then started to go downhill at episode 4...and at episode 5, went even more downhill until episode 12 finally ended the sorry excuse of a season.
I urge people to read chapters 38 - 52 if you want the full experience of the House of Rats arc (after watching episodes 1-3 of this season).
As much as I like this series, everything after episode 3 left a bitter taste in my mouth which just kept getting worse. The job they did on the anime for this season makes it the worst season out of the three...even though in the manga, I felt it was one of the strongest.
If you're a fan of BSD, then definitely watch episodes 1-3. Past that, I'd suggest the manga over this awful attempt at animating the House of Rats arc. If you truly want to watch it, then there are some moments starting in episode 8 and up to 12 which are pretty cool...but it lacked the impact that the manga had, so I can't recommend the anime over the manga when it comes to the House of Rats arc.