Everyone Is Jesus in Purgatory: Newton as a Christ figure (plus Mary-Lou=Mary Magdalene and Bryce=Judas) is a popular interpretation, even though Newton doesn't die. There's also lots of talk about the story as a critique of American materialism.
Freud Was Right: The infamous "gun sex" scene, where Newton and Mary-Lou have sex while firing a gun filled with blanks at each other.
Irony as She Is Cast: When Mary-Lou takes Thomas to a church service and they join the rest of the congregation in a hymn, he proves to be an off-key singer.
Moe: David Bowie's character was this long before it was trendy. Newton also inspires copious amounts of "perverse asexual cuddlelust"; torture scenes and general bad luck aside, he emotes such an intense vulnerability—in every scene—that one is filled with the need to protect him...
Narm: An emotional confrontation between Thomas and Mary-Lou climaxes with him angrily knocking a tray of cookies she is offering him into the air...and in slow-motion to boot.
Also, the random shots of Thomas and Mary-Lou looking into the camera with vacant expressions (Flight of the Conchords referenced these when their song "Bowie" was visualized for their TV show).
Thomas freaking out over the cacophony of the Ominous Multiple Screens: "GET OUT OF MY MIND! ALL OF YOU! LEAVE MY MIND ALONE! GO BACK TO WHERE YOU BELONG!"
Poor Mary-Lou wetting her pants (or lack thereof) when she learns that Thomas is an alien and sees his true form. It's supposed to be a very dramatic and heartbreaking reflection of just how badly shocked she is but it feels like out of place bathroom humor.
Reality Subtext: Bowie was addicted to cocaine and other illicit substances at this point in his life, so seeing him play a character who falls under the sway of substance abuse has this trope written all over it (indeed, the filmmakers were aware of this). Perhaps fittingly his albums Station to Station (1976, recorded at the lowest point of his addiction) and Low (1977, the first album of the "Berlin Trilogy" that unfolded as he gradually emerged from it) got their cover art from photos of him here. As well, the look and to a lesser extent personality of his Thin White Duke stage persona for the former album and tour was adapted from his work here.
Reclusive Artist: Newton definitely counts—he rarely goes out in public and leaves the day to day operations of the company to Farnsworth. Justified as he wants to escape detection ("My life is not secret, but it is private.").
Tear Jerker: One notable example: When Mary-Lou asks what Thomas's children are like, he replies with a mournful gaze across a lake: "They're like children. Exactly like children." And then there's the Downer Ending: After years of suffering he's stuck on Earth, an alcoholic with no confidante or lover who might help him through the guilt and grief he must be feeling. And We Are As Mayflies to him... Tears? This can induce rage.
Ugly Cute: Thomas's true form; when a picture of it appeared on a Bowie fan-blog, one commenter described it as "Voldemort with a nose", and in-film Mary-Lou finds him hideous. But commentators over at YouTube have likened him and his family (especially with their bodysuits) to teddy bears instead...awwww.
Uncanny Valley: What happens when you cast David Bowie as a waif-like alien visitor. Even in his human disguise, the long black coat and hat that Thomas arrived in are... not quite right for the context. When we first see him, he's disguised as human, but his thinness and clothes make him look like a scarecrow, which serves to remind the audience visually of Thomas' otherworldly origin.
Vindicated by History: While the film evokes wildly differing opinions and interpretations to this day and was not a box-office hit, it has enough admirers to not only be in The Criterion Collection, but to serve as one of its first four Blu-Ray releases.
It remains a hit and miss with audiences, but critical opinion of the movie is overwhelmingly positive today.
What Do You Mean, It's Not for Kids?: A science fiction movie starring David Bowie no doubt attracted a lot of teenage moviegoers in 1976, which must have been pretty awkward once the sex scenes got going.
WTH, Casting Agency?: The U.K. trailer warned in voice over "Nothing you have seen or heard about David Bowie can prepare you for the impact of his first dramatic role in The Man Who Fell to Earth." After all, to see an incredibly vibrant and theatrical personality playing an almost emotionless alien would be a surprise...but it worked out quite well for him. Film critics generally vote this or Merry Christmas, Mr. Lawrence as his best film work, at least as a lead.