First off, I disagree with anyone claiming this game is a waste of money - it isn't. I've had it for a long time, but only just recently played it properly and I'm completely hooked. I am a big fan of zombie films so I might be a bit prejudiced, but still, I will recommend it to anyone that likes free-roaming games with lots of surprises.
There's a few things about Dead Rising that make it great: the vast size of the mall (it's kinda like playing GTA but in a mall, basically), the number of zombies you get on the screen at once without any sign of lag, the freedom to use just about anything as a weapon, and the characters. The graphics too, even though not revolutionary are crisp and clear.
The boss fights are hilarious, and the psychopaths are excellent, and quite creepy at times too. The 'acting' is brilliant in comparison to a lot of games, and most of the time it really does feel like you're playing in Dawn of the Dead. But of course there are problems, even though I wouldn't say they're too serious.
The save method is annoying, as there's not many places to actually save, but I feel it can be a benefit too. Yes, you can actually save the game at a point that makes it impossible to complete the story, but it's part of the challenge and you just need to plan the game out more, rather than saving without thinking about it. Also, returning survivors to the security room is a real pain, since it takes a lot of time and uses a lot of your weaponry and health, just to get right near your destination and have the survivor swamped by zombies and eaten alive.
But putting small faults aside, Dead Rising is a brilliant free roaming horror fest that covers a lot of ground that Resident Evil hasn't (plus, it has a much better zombie movie feel to it that Resident Evil seems to have almost completely strayed away from). If you like zombies, and survival horror games, but prefer to play seriously, buy Resident Evil 4. If you like the above, but also like to have a lot of fun with your gaming, buy this.
Dead Rising, in a way, is the Mario Kart of the survival horror genre, and a damn good game too.