Saints Row The Third is one of my favorite games. They put a bunch of people in a room to come up with absurd fun and didn't tell them “no” this time. As such I have been waiting with anticipation/pain during the development saga of Saints Row IV.
The game that came out of this torturous process is more than the DLC that people have been fearing but does feel like less than a full game. Most of the side missions you get from your crew are to do all the instances of the activities scattered through town. Having finished all the activities and diversions when they became available, to level my character the, the back half of the game was a lot of just talking with the crew to get the rewards for “completing” the task.
I also had some issues with the game locking up every few hours. The frequent check pointing made it so I never lost much progress it was a hassle.
The issues aside this is still a great game. Flying across the world doesn't seem to get old as you progress through the game. Also you get a lot of story and background filled in about the crew and people you encounter from the previous games. They also continue with making fun of anything and everything. Including a parting shot to THQ.
A working knowledge of the previous games is definitely a benefit so you know and can appreciate all the characters they have brought back to life.
If you haven't yet played Saints Row The Third, that would be a better place to start.