Often some units will not respond to Concentrate Fire. This is because they were already busy at the time you issued the command, usually with reloading or finishing a firing sequence. Concentrating fire circumvents the reload time of bazookas and mortars, allowing them to instantly fire again.
Concentrate fire is NOT effective when your infantry units are equipped with low fire rate and/or low capacity weapons like the Springfield since after one or two shots the soldiers will reload and target another enemy, potentially leaving the threat just pinned and not dead. It is much more effective with automatic weapons and large groups as your men will provide much larger volumes of fire towards the target.
Concentrate fire can work against cloaked units like the German Sniper or the Brandenburg Infiltrator.
Vehicles do not respond to Concentrate Fire.
If you use concentrate fire on an enemy in the middle of CQC with one of your troops, you possibly can save his life if he is losing. This can also lead to the unit not being able to fire for some time.
If by some means you manage to concentrate fire upon a corpse, you will get the message "This German is dead already, give him a break".