Author Existence Failure: A famous example. Bela Lugosi died after filming only a few seconds of footage completely independent of the plot, and was rather obviously replaced by Wood's wife's chiropractor, who covered everything below the eyes.
Beam Me Up, Scotty!: Eros never said "A particle of sunlight contains many atoms!"; the actual quote is "A ray of sunlight is made up of many atoms!"
No Budget: Wood was so far over his head in producing the film on $25,000 that it's hard to really put into words how badly it turned out.
Cheaply built sets like the graveyard and plane cockpit either suffered from technical inaccuracies or (in the case of the former) were prone to falling over when the actors got too close to them. Props and set pieces were also reused between scenes, which explains why the interiors of the flying saucers have wooden desks and radar equipment, or how their exteriors reuse the interior's walls but inverted.
Speaking of the flying saucers, they were store bought miniatures that Wood had repainted and suspended with incredibly visible fishing lines. They would frequently wobble around and occasionally casted shadows on the backdrops whenever they moved.
Wood would use whatever stock material he had at his disposal and shot most of Plan 9 without a second take, causing many of the above mentioned goofs to make it in the final cut. He was also limited with the amount of zombies he could afford to hire (hence why there's only three in the movie) and often reused shots involving Bela Lugosi or the saucers to further pad out the film.
Science Marches On: What appears to be another of the film's science blunders is Eros stating that after the H-bomb, the only explosion left to be discovered is the Solaranite, which has a pretty major omission in that no one in this universe seems to have conceived of an antimatter bomb. It's hard to entirely fault Wood for not adding this in, however, as almost nobody outside of the scientific community had heard of antimatter in the mid-50s.
The Shelf of Movie Languishment: While it was completed in 1956 and had a private preview screening on March 15, 1957, it didn't get released until July 22, 1959. Distributors Corporation of America picked up the film and planned for a Spring 1958 release, but the company folded and the film languished another year until DCA's receiver, Valiant Pictures, got around to releasing it. note (However, if IMDB's trivia page is to be believed, the film was already in limited distribution by June 1958 through DCA.)
Strange Minds Think Alike: This film has a lot of similarities with Invisible Invaders. In both films the aliens are scared about the humans experimenting with weapons of mass destruction and technology they don't truly understand, so they reanimate corpses in order to kill the living until humanity surrender. Both films were released in the same year and although 'Plan 9...' was filmed 3 years earlier, 'Invisible Invaders' appeared on theaters a month before. At first 'Invaders' got much better reviews and became a TVCult Classic, but the film felt into obscurity while 'Plan 9' became a huge cult sensation in the 80's.