I have always liked, yet hated TSFS. I like the story, yet I hate that my favorite character, the Enterprise herself, is killed off.
Politically, the Federation must be run by complete peaceniks who are utterly incapable of a self-preserving thought. The Genesis/Mutara System is within Federation space, and even though quarantined it is such a peaceful sector that a mundane vessel such as Grissom can operate.
So, using modern terms, Genesis is in a home countries (Federation) waters. Enter the Klingons, who use a submarine to sink vessels in hostile waters and send a raiding force to claim land/capture people. If a Russian Sub were to do such an act in American waters (take a backwater/sparsely populated area like Midway Island, somewhere in the Aleutians or Alaska) it would be seen as an act of war.
Instead, the Federation suffers the loss of two naval vessels, then lets the Klingon Ambassador present his version of the event (complete with threats, release of battle footage and Genesis materials) to the Federation Council, who are acting like timid sheep until a Vulcan of all people (Sarek) has the gaul to step up to the challenge.
But anyway, back to TSFS. I've thought of so many ways that they could have done things differently instead of blasting Enterprise to Kingdom Come. As someone mentioned before, they could have used the transporters more creatively. Did these transporters not have the "scrub" that TNG had that removed weapons detected from the pattern? Scottie could have used his transporter expertise to send the Klingons to the Brig, to deep space, anywhere. Chekov despite not being an expert at Uhura's comm station should have been able to trianglulate the location of the ground party. They beamed down within a short hike of them, so they had to know where Savvik, Spock, and David were. They could have beamed them directly aboard the Enterprise then carried on the fight (manned select stations, got weapons active, etc). Since the BoP's shields were down Scottie could have beamed a chunk of matter into the antimatter tank, or he could have beamed aboard the Enterprise the BoP's "gas cap" (for lack of better terms), leaving her powerless.
Kirk and Co could have fought aboard the ship. Kruge expected opposition, thus he ordered his crew "armed heavily". Still, despite their arms, Kirk and crew had knowledge of every part of the Enterprise, their home ground. Have someone set up to fire in the transporter room as soon as they beam aboard. Fire at them in the hallways. Get additional arms from the ships arms locker to repel boarders. Hell, the Klingons had to get on a turbolift to get to the bridge, why not lock them in there, send the lift to the shuttlebay, then open the doors?
Sulu accurately guessed the compliment (about a dozen officers and men). They would have seen that the Klingons were stretched thin after eliminating the boarding party. There were not enough Klingons left (split between the BoP and the planet) to have put up a fight. Some of the Enterprise's crew could have manned a Phaser turret or rearmed the torpedo launcher, returning the ship to the fight. Scottie could have restored some control of the automation center as well.
Also, Starfleet had more than enough reason to vector additional ships ASAP to the sector. Contact had been lost with Grissom and a stolen battle-cruiser with a rogue crew was en-route. Kirk and Co could have beamed aboard Savvik and Spock, then been fighting a desperate fight against Kruge and Co onboard the Enterprise (instead of planetside), Kirk still kicks Doc Brown in the face and down a turboshaft, then the BoP is in position to fire and kill when the Cavalry arrives. Enterprise is saved, BoP is captured/destroyed and Kirk and Co go to Vulcan with Sarek (who was with the Cavalry) to end the movie.