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Initial cavalry charge scene, actually seemed rather correct. Horses will continue to ride through each other's formation and it will be very chaotic violent. Collisions between horses will occur. It would have been incorrect if like in most media the cavalry instantly stop and start having 1 on 1 duels with each other while on horseback. Cavalry charges have a lot of momentum. What was unrealistic is both sides lose all of their horses. In real life, the Stark cavalry would have turned around to regroup because they were so outnumbered. Meanwhile the Bolton cavalry would have taken both flanks for pincer movement (which could conveniently occur since the battlefield was not where the Starks built flanking countermeasures). They likely killed off all of the horses early on for budget and film reasons. The scope of the battle started large with multiple combatant types, which quickly shrank to one small enclosed area.
The phalanx formation - The way it was executed with a pavise shield bearer and extremely long pikes in the rear did not happen as far as I know. Late medieval battles did have more and more pikemen present. The shield and spear wall was a very important aspect of earlier medieval battles, but each individual had a spear and shield. The Battle of Cannae seemed to inspire the double envelopment leading to a human crush and stampede. During the battle widespread panic caused the Romans to compress so much they could not effectively fight and they were annihilated by the Carthaginians.
The piling up of bodies was just fantasy. A 10 foot high wall of corpses is just not going to happen. Yes, in historic medieval battles clutter of corpses did make terrain difficult. But a hill of dead? No. Not to mention the Bolton archers firing indiscriminately into the backs of their own men. Yes, it could and did happen but never with the intention of building a corpse wall. It was extremely unwise to shoot the backs of your own knights and cavalry because they were the elite of society and your best soldiers. Not to mention it could invite your cavalry attacking your own archers. At the battle of Crecy, the French knights charged down their own crossbowmen (for a lesser offense of cowardice and simply being in the way). Doing this also invites a dagger to your back next time you're alone with a few of the knights who lost kin to your archer's arrows.
As for the final charge from the Vale into the rear of pikemen, yes that's going to be devastating. Pikemen are vulnerable to being flanked if not supported, and a formation of heavy cavalry hitting their rear will destroy them. Historically, Alexander the Great dominated with his pikemen and cavalry tactics, but once he died and his Diaodachi overly relied on pikemen and not multi unit formations they were defeated en masse by Romans flank attacks and terrain disadvantages. I'd also have to add thousands of cavalry suddenly showing up is also unlikely because it is a huge mistake to not have any scouting forces or advanced warnings. Suspension of disbelief would have to have us believe that the Bolton scouts and sympathizers were neutralized.
It really just wasn't.
It was a mish mash of different era's, and development levels, but then fighting in a poorly contrived plot point. Looks cool but no more true to how a Feudal levy of any time might try to fend off a large force of raiders essentially. You should lend it no more credibility than the first battle in Gladiator.
And this really speaks to GRRM's one real flaw as a writer, translated to the show, he is great on a personal level usually, but not so great when it comes to the actual flow, pace, and nitty gritty of the fighting. Westeros is a ham fisted miss match of about 500 years of European history(you get later as you go South) but then they all still end up fighting in similar ways and armies which would have no shot against each other do fine. His pacing is also very accelerated.
The two bad parts are the dead bodies(no we have no evidence ones that large ever formed, but like GoT a few exaggerated stories that include them: https://www.reddit.com/r/AskHistorians/comments/4oyq3u/last_nights_got_had_me_thinking_about_a_question/?
While the abortion of a Phalanx/Shield Wall/Pike formation was just a travesty. Men didn't fight like that ever, it would have been counter intuitive(consider how effective it was when the Bolton's put Stannis's army to flight and just hunted them, compared to trying to fight and kill all of Jon's force then and there). https://www.reddit.com/r/AskHistorians/comments/4oyr35/how_realistic_was_the_recent_game_of_thrones/
And while cavalry charges could and were deadly, that is an obscene amount of knights that the Vale is somehow is able to support and equip. While culturally they might be disposed towards a force of heavy cavalry economically it makes little sense. Switzerland for instance was also prosperous mountain valleys, but instead of lots of knights Swiss mercenaries were one of the first to take pike and infantry formations to a fine art, separate from Sergeants or Men-At-Arms fighting on foot.