Loose Threads:

How does Brittany know any military tactics? And where she's learn words like "terrain" and "ambush"?

If Mr. DeMartino went to military school, why can't he hit a stationary, human-sized target at close range?

Did anyone ever win the game(red or blue)?

Notables:

The title is a parody of "The Deer Hunter," a Vietnam movie.

Kevin's father is a contractor.

Jake is getting more reluctant to allow himself to get drawn into arguments between Helen and Daria.

"When Johnny Comes Marching Home" is a Civil War song about a soldier returning from war.

Mack's olive-drab fatigue is a lot lighter in color than everyone else's.

The Fashion Club members are wearing black outfits that vaguely resemble SAS (and various other special forces) uniforms rather than the more common olive-drab and jungle camouflage.

There is a huge time delay between Kevin saying something stupid and Brittany beating on him (possibly because of the scene shift, but not totally).

Mr. O'Neill is wearing a peace sign and a happy-face button on his shirt during the war game (possibly a reference to "Full Metal Jacket", where one soldier wears a peace sign and paints Born To Kill on his helmet).

Daria's sullen monologue -- "Hell is the impossibility of sanity... it's only been an hour. Some hour, grandma.." -- is from Platoon. Guess she's a war movie fan.

Helen's assistant is probably named Stephanie, although she may be Eric's assistant.

Jane said "I stopped to wipe out a village of farmers," which refers to the My Lai massacres.

Quinn, Tiffany, and Stacy shoot at Sandi thinking she's Quinn's "cousin", even though they aren't even wearing the same color clothing (black/dark gray on Sandi, olive-drab on Daria... a difference you'd think they'd spot).

Kevin gets shot on his shoulderpad and still complains about it stinging.

When Sandi is outside and takes aim at Quinn through the hole blasted in the side of the building, it's a reference to Full Metal Jacket. 

Helen is very insecure about her appearance and age.

Mr. O'Neill and Mrs. Barch make out (probably do rather more than this, really).

When Quinn's fashion club nemesis is left behind it's an imitation of Willem Dafoe's dying seen in the movie "Platoon" (complete with the Samuel Barber "Adagio for Strings" music.)
It also parodies a scene from "The Deer Hunter", and something similar is seen in "Rambo II".

When Jake is in the tunnel at the end and says "The Horror", it is a reference to Apocalypse Now.

Mistakes:

Helen's writing pad is empty even though she was writing on it.

None of them actually wear real paintball masks or have actual paintball guns (they look more like Super Soakers), although Mrs. Li's mask is close.
While full masks are more desirable most paintball fields allow player to play with only goggles. Most paintball safety masks are little more than motorcycle safety masks with a protective plastic plate for the lower face area. Infact, most paintball safety gear is made by motorcycle safety gear producers (JT, Scotts, Vents). anyway, on most standard paintball masks the plastic face shield is removable, leaving only the goggle section of the mask.
East coasT

Jane tosses away her paintball gun, but is later able to shoot Daria anyway (everyone seems to be tossing their guns around).

Jane's paint stain is gone not too long after she is hit.

When Mr. DeMartino starts shooting at Brittany, he's crouched behind a rock. When she handsprings to him, he's standing up with no rocks in sight.

Daria and Jane change back to their regular clothes without stopping. They also didn't seem to even bring their regular clothes with them.

Miss Barch's armband is missing when she is stuck with Mr. O'Neill.

The rainbow is missing a few colors.

Daria is tan sometimes, pale other times.