This app was mentioned in 2 comments, with an average of 1.50 upvotes
I'm guessing the app isn't grabbing a wakelock, partial or otherwise, meaning there's nothing stopping the CPU from ramping down to save battery when the screen is off. CPU slows down, leading to a stuttery and janky experience for you.
Which apps have this problem? GPM doesn't seem to stutter, though it's running on newer hardware (my Nexus 4). Even my Galaxy Ace ran Cloudskipper smoothly, though; I'd recommend giving it a shot (however briefly) and seeing if there's any improvement.
Are you rooted or using a custom kernel at all? Either of those mean you could have set the processor to slow down when the screen is off.