The Helicarrier,even damaged,still had quite a few jets and such on the deck.Why not sent them to the battle where they'd make cannon fodder out of the invaders?They have the toys,use them.Loki's little army wasn't that tough when it came down to it.
Apparently, the real reason behind this was that the filmmakers couldn't get Pentagon backing for the film. Only Odin knows why.
As for an "If Only" List.
Keep the scene with Maria Hill being debriefed by the WSC. Actually, just more Maria Hill. Damn, Cobie Smulders can play a BAMF so well.
Cut the whole Black Widow "redemption" thing, or leave it unresolved. She must not have had a whole lot of "red in her ledger" if it was balanced out by knocking a guy's head on a railing. This would be much better suited for a Black Widow or SHIELD movie (say, she goes rogue in the middle of a mission to complete some unfinished business, yadda yadda yadda).
Stronger SHIELD involvement in the Battle of Manhattan. Hell, even if there was no Pentagon backing (and thus Pentagon jets), CGI-ed in air to air missiles streaking in from beyond visual range (as would be realistic) and clearing the skies of flyers for a short period of time would be perfectly doable. And having SHIELD troops who for once don't get wiped out in droves would be pretty cool.
Cut the runtime of the Fury-Rogers-Stark pissing match during the midpoint of the movie. It was important, yes, but it ran a little long and could have been streamlined some.
More Army and Police involvement in the Battle of Manhattan.