Xbox 360 users with a Mass Effect 2 endgame save stored in the cloud are going to run into some issues when they try to bring that character into a new Mass Effect 3 game. An Electronic Arts support page notes that endgame saves from ME2 can't be imported from the cloud into Mass Effect 3. What's worse, the fix won't be as simple for some as copying the old save back to your local storage.
If you're playing ME3 on the same console you completed ME2 on, you're safe. Copy the save to your local storage and import from there. If you've upgraded or changed consoles, however, you'll need to download the cloud save back to the old console's hard drive and then transfer it to the new one using a USB stick, transfer cable or memory card. In other words, if the old console isn't available anymore, you're out of luck.
EA suggests that it might be possible to fire up ME2 using a locally stored save and "re-finish" the game, the article states that "we unfortunately cannot guarantee that this will work with certainty." There's no mention of work being underway on a patch to fix this issue, though affected players can certainly hope. There's an acknowledgment that affected players are probably pretted pissed though.
"We understand this may be a great setback to those impacted who have been following the Mass Effect franchise over the years," the support page reads. "We thank you for your patience."