What specific effects can playing Mass Effect Infiltrator have on Galaxy At War in ME3?
Completing Mass Effect: Infiltrator increases your Military Strength by 40. There are no other benefits from playing ME:I that are reflected in Mass Effect 3.
There are three permanent Galactic Readiness bonuses.
One for finishing the game (once), one for getting gold on all Main Story checkpoints, and one for getting gold on all Turian Story checkpoints. You can fill all your State of readiness with the ME:I.