I'm going to be the odd man out here, but I was largely unimpressed with it. Maybe it is because I don't find reference based humour all that funny, and to me, it seemed like that was all this game could pull off.
The superpowers were fun, but they completely destroy other elements of the game. Why do I need a car when I can run faster than one? What do I need a plane when I can jump and glide? The fireball, when fully upgraded completely makes guns useless. A fireball that lights people on fire, who explode when they die, which lights other people on fire, and so forth.
They said they were going to make the game more "vertical", and we got five towers to climb, and if you tried climbing the massive tower right in the middle of the map, you get about halfway up and an invisible wall blocks you off. A lot of the "new" clothing was just the stuff from the DLC from the last game, same with cars.
A lot of activities were removed, just to be replaced with different versions of the same ones. Here is mayhem with a tank, now here is mayhem with a ufo, mayhem with a rocket launcher...with a mech....with superpowers...
The game was fun and amusing in parts, like the Predator reference at the start, or the Splinter Cell mission (which was funny for the first few minutes...then it kept going....), but it just felt so lazy and forced. OH, people though the Burt Reynolds bit was funny in Three, so let's drag that joke out throughout the entire game with Keith Davids. People liked the singing along to the radio joke, let's do that a few times in a row. And the constant jabs at Mass Effect, and Mass Effect 2 in particular was just weird,and actually felt a bit bitchy. One of my friends playing Saints Row 4 never played Mass Effect, so a massive chunk of the games humour went over his head.
As I said, I enjoyed parts of the game, but a lot of it was rushed, served only to drag out the game, and not really funny. Again, maybe it is just my sense of humour is different to the games.
Also, no mission select again? I'm not going to play through the entire game again just to do one five minute section I liked. I thought the developers had noticed that was one of the main complaints about about Three.