In real life, Criswell had a speech impediment, and couldn't pronounce certain words. He had to write all of the narration himself, because only he knew what he could enunciate properly. This is why he delivers his dialogue so oddly.
The Reality Subtext of Bela Lugosi's death makes some of the opening narration less funny. The part about how death is a shock even when we know it's coming is very likely a reflection of Ed Wood's reaction to losing his friend. It's particularly poignant in the clip of the Old Man smelling the flowers outside his house, and leaving "never to return again."
Ed Wood's cameo as a drunken bum, which is pretty much what he would become in his later years.
Inferred Holocaust: Humans learn nothing, and it's implied that they'll do exactly what the aliens feared, hence Criswell's warning at the end. Plan 9 is to stop humanity building a "solaranite bomb" and destroying the universe. Yet Plan 9 fails. What does this mean for the universe? Given that it's the Plan 9 Universe, total destruction may be merciful.
"You see? YOU SEE? Your stupid minds! Stupid! STUPID!"
Tor Johnson's damn blank-angry face when he becomes a zombie has achieved this status, even becoming a mask!
Narm: One of the zombies is constantly covering its face.
Older Than They Think: Criswell's opening line — "We are all interested in the future for that is where you and I are going to spend the rest of our lives" — is often held up as one of Wood's classically clunky lines. In actual fact, Criswell used that as the intro line for his TV show for several years before Plan 9 was filmed (and continued to do so afterward), though he usually gave it a much wryer delivery than he does in Plan 9 — witness it in action in his appearance on the Johnny Carson New Year's Special in 1966. In fact, all of the narration was written by Criswell himself.
Woolseyism: The fact that some subtitled and dubbed versions have better writing than the actual movie is less of a show of the translators' skills and more damning evidence of the movie's own ineptitude. Just being able to truncate the redundant dialogue and make some phrases sound much more natural is an improvement already.