First off, I should note that I never played the video game, and if there were allusions or references, I didn't get them. Nor did I feel like I was missing them. There weren't really any moments where something made no sense or felt like I was on the outside of an inside joke.
Overall, the movie was about what you'd expect: good fun, good action, and not much depth. The story, characters, and set pieces all felt like a melange of bits from other movies. Lots of characters and story elements felt like they matched up one-for-one with things from Star Wars, to the point that at a few moments I recited in my head the line that someone said at that point in "the original" and the line that followed was very similar. There were also many scenes that put me in mind of Raiders of the Lost Ark, and other bits reminiscent of dozens of other movies. But lest this seem too harsh, it was never distracting, never really came off derivative; it was more like a pastiche, so you could either not notice the similarities, or if you did, they came off as appreciative.
On the downside, far too much of the action followed Hollywood's long-standing crush on the shakycam, the extreme close-up, and other methods of making sure that the poor, hard-working fight choreographer goes unappreciated since you can't really see the fight. In keeping with the video game's history as a platform game, Dastan does a lot of acrobatic jumping, and Jake Gyllenhall trained in parkour for the movie, but we often don't get to see the stunts very well either -- the shortish sequence in Casino Royale showed parkour better than the many longer sequences in Prince of Persia due to the cinematography.
There was also some editing that seemed jerky, particularly near the end. To avoid spoilers I won't say which scenes I mean, but there are two right at the very end that both seemed rushed, with things happening far too fast for their dramatic importance. Maybe that's just how I felt, though.
The acting and casting were solid throughout. Sure, Jake Gyllenhall doesn't look very Arabic, and one can't help wonder what someone like Naveen Andrews might have done, but you're really not going to be worried about that. Gemma Arterton doesn't look very Arabic either but I, for one, didn't mind seeing her one bit. (She was certainly better used here than in Clash of the Titans.) No one's acting stood out, but everyone's was solid.
The male and female leads had the obligatory love-hate relationship, with interleaved bickering, moon-eyes, treachery, almost-kissing, and more bickering. Often, when you see that storyline done, it's perfunctory and uninspired, and in a movie like this you expect it to be paint-by-numbers, but it's done really well, largely to the credit of the actors. Doesn't hurt that the dialogue didn't come across as the characters just being sassy because of being sassy, but because of having real reasons to believe and act as they did. (Even if Tasmina tended to describe so many things as "sacred" one expected her to start going on about how her breakfast cereal was sacred after a while. In another life she'd be a Minbari.)
If you want some light entertainment to eat popcorn to, this is a great choice. It's probably one of those movies that you'll want to see on a big screen for the sake of the action sequences. It's not something that'll take up residence in your mind though.