And "these aren't the Orcs from LOTR" is very much correct. These are, according to the book, pretty much "big goblins". Those in LOTR are Uruk-hai, especially bred for war and infused with magic to make them stronger, and well-prepared with an industrial machine behind them.
As for the 12 people turning the battle...Firstly, it's 14 (13 dwarves and a hobbit). Secondly,
in the book, it's 500 orcs, one village of humans, and one company of elves. Yes, even so, 14 people won't really "turn the battle", but it's 14 people, decked out in super duper armor with shiny new weapons, coming out of nowhere, reinforcing an army of practically peasants with pitchforks, badly armored dwarves with hammers, and a few elves, who get reinvigorated by the sight. This wasn't actually a very big battle, it just
sounds huge because the book's written from Bilbo's POV and he's retold the story a bit bigger every time. The movie...Well, I guess that's the 10,000th time he told the story
Tactically, yes, jumping over the spear wall made no sense whatsoever. Nor does then charging into the back of your allies.
In all, these shortcomings are really only such because PJ tries to make it all more "epic" and "grand" than it actuall is in the book. It
isn't a huge clash of a mountain of orcs against a people. It's a skirmish of, in all the 5 armies combined, maybe 5.000 people and an equal number of beasts. (also, in the movie I thought it was Dwarves/Elves/Humans/Eagles vs Orcs, where it's actually Dwarves/Elves+Humans/Eagles vs Goblins/Wargs in the books. Clearly!)