Imagine that someone invents a machine that makes omelettes: brilliantly-colored, spicy omelettes made with breathtaking speed. Taken by its combination of verve and simplicity, you order the machine. But when it arrives, to your dismay, you discover that the omelette-making process is actually fraught with danger--80% of the time, due to a misstep in the instructions, it sets your kitchen on fire. Also, for some reason, the manufacturer has added a mode for making breakfast sausage instead. The machine is a very poor sausage-maker, but it keeps getting stuck in sausage-making mode, and until the sausage is successfully cooked you can't get back to the omelettes (and the kitchen fires, which are starting to lower your enthusiasm somewhat for the whole idea of breakfast).
Mirror's Edge is this omelette-maker. It's filled with absolutely gorgeous visual design, presenting parkour from the first-person perspective. Except that it doesn't work, about half the time. The controls are overly touchy, especially strafing, and the context-sensitive options aren't nearly sensitive enough. Worse, the part of the game that's really fun--the running, in between falling--is interrupted regularly with fight scenes. Often, you can't run from the fights, because the soldiers are very good shots and the escape routes are (intentionally) via slow and exposed pipe-climbing. It's like someone on the design team said "We've really got something here, with the running part of the game. Let's make sure to take it away from the player on a regular basis."
There's always a lot of comparison to Prince of Persia whenever a game tries free running and acrobatics, and with good reason, since it did it best. But people often take the wrong lessons from this, citing the "rewind" function that largely canceled out dying-as-punishment. That wasn't the genius of the gameplay, however: what made it really good was in fact the inaccuracy of the controls, the way that the Prince would do the right thing as long as you hit a button with something close to the right timing. PoP realized that the fun wasn't in being a precise platformer, but in the simple thrill of directing a complicated flow of leaps, grabs, and wall-runs around the game's carefully-crafted spaces.
It's strange, actually, that a title with such aggressive visual editing as Mirror's Edge--it's practically monochromatic--would have such weak editing on the interaction side. Eliminate combat from the mix, and you've cut the game down to basically two buttons, up and down. Get rid of strafing while you're at it, since all it does is let me swerve off catwalks by accident, and make it work more like the first Metroid Prime games (which also took a third-person gameplay conceit and moved it into first-person). Those changes would work the level designers a bit harder, but the end result is leaner, more focused gameplay.
What it all comes down to, really, is that when asked to make a choice between realism and fun, Mirror's Edge chooses the former. No doubt, in real life, Faith would be riddled with bullets almost instantly, and so in the game, she is. As a result, the player is discouraged from approaching situations with speed and daring, because it's a process of trial-and-error fatalities made worse by Faith's clumsiness. By contrast, it would be highly unrealistic for players to be able to sprint through a gauntlet of enemy fire, bullets whizzing by but rarely breaking the flow of action--unrealistic, but much more rewarding. As it is, the game just feels unfair: it gives you the tools to do one thing fairly well, and then punishes you for trying to use them.