Just doing a replay.. the game actually isn't that bad. It's a very fun game and has a lot of good comedy moments and some nice impactful ones. (Plus, the voice acting! The line "Ok unicorn, you asked for it!" made me crack up)
The problem is, well.. it needs those more serious moments like SR2 had. I mean, a moment I remember is the whole Aisha's funeral bit. Running around and mowing down waves of enemies doesn't say the Saints are brutal, it says it's silly. Now a funeral interrupted, and instead of fighting they tell him to back off. Then when he refuses... a horribly extreme form of disproportionate retribution is done in a moment that not only says "We're hardcore" but "Do NOT fuck with the Saints, or you will NOT live to regret it.. for long."
It needs more a down to earth feel. It's not about realism or what, it's about pacing and thematic effects. It feels like they forgot some of that when they did the third game, and went for something big and bombastic, while the second probably had a better story and staying power.
Well, ok, it had 3 stories, and a fourth addendum. That's one thing I liked in SR3.
The biggest fault though is length. SR2 had more to do. Making the activities non-optional (by being required story-chain bits) wasn't a good way to pad out stuff, but I understand it lets people see how they work. Making them not required as locks to progress the game, that was a good move. I just wish they hadn't chopped out a dozen of them as they went.
So, ways to make a good SR4? Pace out the plot, make it more deeper again, go back to SR2 and see how it flowed. Then, add side activities again.. the hardest part is setting them up, once it's done it's relatively easy to extend it, although the voice acting budget would eat up a good chunk (a move I liked.. that quote is from the last Deckers mission... and you only get it if you make a 'wrong move' in the one subgame. The whole game in general has different quotes by the different voice actors and for different parts). Still, that's a benefit, it makes them feel a bit more like different people in a sense.
The key strengths are already covered.. automotive carnage and fun that's emergent from the design. The next step is the plot.. don't take youself too seriously, but at the same time, realize that you don't have to make it all over the top all the time, or you can't go further. The entire first half hour of the game is amazing. It shouldn't have been at the start, because there's no way to top yourself, and it just makes the rest of the game look a bit of a let-down in comparison. The game should have built to that.