I have to admit, it's still kind of bugging me that we don't know how Fisk got out of prison and has a restored reputation since DD season 3.
Responding to you and @ladymaigrey who also asked about this: yes, it's frustrating and feels too comic-book-ish.
I might pick up on more details as I rewatch the show. But my understanding at this point is:
He's appealing his charges and/or sentence from S1; and
He was acquitted of his charges from S3.
The implications of this are huge.
First, if Fisk successfully appeals his charges, that would mean the prosecutor would likely have to start over and present the case again. It's possible that the prosecutor would simply not do so because it would be too much work, because it would be against public opinion, because Fisk bought them off...maybe the appeal would be based on bad decisions from a judge, and the prosecutor knows that Fisk has bought the judges off, so bringing the case again is fruitless...maybe it's just that Fisk's lawyers have so much money that they bury the prosecutor's office in frivolous motions and the prosecutor can't justify spending so much of their budget on one man....
As for his charges from S3, an acquittal means Fisk went to trial and the jury found him not guilty. Which, oh my goodness. If the reason he was acquitted was "because of the FBI," that suggests that the jury...got confused, and thought the FBI's corruption meant Fisk wasn't guilty? Or perhaps the jury was pissed and engaged in jury nullification and acquitted Fisk because they were angry at the FBI's corruption? Or perhaps the jury just hates prosecution and will always find any defendant guilty because they think the system is broken, and that got interpreted as an acquittal because of FBI corruption? Or maybe someone in the jury was bought off, and persuaded everyone else to acquit, and then claimed that it was because of the FBI to hide the fact that they were bought off?
And I am fascinated by the idea of Fisk being acquitted. I love juries, but goodness, they are just twelve random people and they they can be dumb. The average reading level in the U.S. is 7th-8th grade. The average attention span of an adult is 45 seconds. Jurors can completely fail to connect two logical points; they can stop paying attention and miss key information; they can conflate issues; etc.
Juries can (and do) also choose the absolute wierdest possible hills to die on and think jury duty is an opportunity to make some kind of statement. "I hate the FBI [or the police or prosecution or The Government™ or whatever] and therefore I'm going to find this person not guilty" is absolutely a thing that happens.
I love juries, I really do, and I would never want to replace our jury system with anything else. But they are fallible.