In shots of CBGBs, many of the punk extras have piercings in their tongues etc. Tongue piercings were first performed by Gauntlet in San Francisco, and not popularized until the '80s. Similar stories are true of eyebrow piercings and many others. During the late 70s and most of the '80s, piercings as featured in the movie had little to do with the punk scene, but were embraced by the gay/S&M scene.
While Vinny and Richie are sitting in a diner and the two guys in pink shirts are hassling them, the song "Psycho Killer" is heard as if on the diner's jukebox. The album (Talking Heads 77) upon which the song is featured wasn't released until Sept of 1977.
The Son of Sam killer is shown wearing a camouflage field jacket which has on the left breast a black Velcro backing designed to hold a removable "Aircrew" style ID patch. This was exclusively issued to US Air Force personnel in the early to mid-'90s.
During certain parts of the movie, Richie is wearing black combat boots that did not become available until the US military adopted the Battle Dress Uniform (BDU) in the early to mid 1980s. The boots in questions are officially designated "Boots, Combat; Mildew & Water Resistant, Direct Molded Sole" and were "standardized 30 Oct 1984."
Vinny and Dionna are seen partying at Plato's Retreat. This is supposed to take place in the Summer of 1977, while Berkowitz was still on the loose. Berkowitz was apprehended in August of 77, and Plato's retreat didn't open until September of 1977.
When the guys come to get Vinny to help them with Richie, Vinny picks up the phone to call the police. When the phone is ripped off the wall, you can see that there is no phone line or place to plug in the phone on the wall.
During the shooting sequence where Phil Rizzuto is doing the play by play for a Yankee game, you can clearly see blood mechanically squirt out after both victims are not moving and no more shots are being fired.