The natural advantages of the PC over consoles (assuming that the game uses both) might unbalance the game. Shadowrun countered this rather well by making PC users lose accuracy when turning quickly, but it's still a problem. Also, PC users have access to mods. From mods that change the game's GUI to ones that let you see through walls, these players would have an unfair advantage.
On the other hand, if it's compatible with, say, the Xbox 360 and the PS3, then anything done to one game would have to work on the other. Any DLC would have to be released for both. Any updates would have to be written for both and updated at the exact same time. Still, while releasing a game for the PC and consoles would be difficult, having multiple consoles would just be challanging but doable.