Actor Allusion: The first thing Envy says upon meeting Ed is "Arara", an expression of surprise and interest. It is often uttered by Conan Edogawa when he's playing dumb.
Adored by the Network: Brotherhood has essentially replaced the original anime, which has not aired ever since [adult swim] started airing Brotherhood (and which AS no longer has the rights to). It stayed when [adult swim] Action was replaced by the revival of Toonami, and so far, as of January 2014, Brotherhood (along with the long-running Bleach) has the distinction of being the only show on Toonami that has managed to stay on the lineup ever since the block was revived.
The Cameo: Aaron Dismuke, English voice of young/teen Al in the 2003 series and The Conqueror of Shamballa, appears in a brief role as Young Hohenheim as he couldn't reprise the voice of Al (due to his voice obviously breaking).
Fan Nickname: Due to his lack of name, fans had to be rather creative with giving the gold-toothed doctor a name. Some variations include "Bastard Doctor with the Gold Tooth," "That Bastard in White," "Gold-Tooth Bastard", or "Bastard Doctor Who Slit Riza's Throat."
Keep Circulating the Tapes: Funimation lost the license to Brotherhood on March 31, 2016. Hope you didn't put off buying it before then.
Brotherhood replaced a good deal of the Japanese voice actors from the first anime. Two who returned ended up playing different characters. In contrast, the English dub retained nearly all of the original voice actors; the changes basically amount to Al, Scar, Hohenheim, Marcoh, and Breda.
Brotherhood is not the only instance of Gundam and Fullmetal Alchemist sharing several voice actors, the original anime also featured several seiyuu from Mobile Suit Gundam SEED. So it's probably a safe bet that if there is a FMA anime, then they will most likely follow after a Gundam series, and have several voice actors in both.
Screwed by the Network: Important bits of the plot have been cut for time from the [adult swim] broadcast, particularly regarding Mustang and his group after he makes his move just before the Promised Day.
Cross-Dressing Voices: Ed and Al are voiced by women in Japanese, but not in English. Envy, however, is voiced by a woman in both versions. It contributes to his/her/its creepiness quite effectively.
Cut Song: "Melissa" (the first opening song) and "Undo" (the third) were unused in the North American airings of the series; "Ready Steady Go" (the second opening) replaced them instead, with the opening finally changing once "Rewrite" (the fourth) comes along in the final stretch of the series.
Development Gag: Travis Willingham originally auditioned to play Armstrong, and uses the voice he took on for that role in the line "I love dogs!"
Vic Mignogna on many occasions was not actually shown the entire script, and his lines were all recorded in chronological order. As a result, his surprise at what was on the other side of the Gate of Truth and what originally happened after the Shou Tucker incident, and Vic's sadness in the last few episodes, were legitimate reactions.
When Al was hit with a teacup, supposedly, a teacup was tossed at Aaron Dismuke's face.
God Never Said That: Bordering on Hate Dumb, quite a few members of the manga/Brotherhood fandom seem to think that the changes in the anime were made with no input from Hiromu Arakawa and that she disapproved—if not disowned—the whole thing. In reality, Arakawa not only greatly approved of the changes, she actively encouraged them (mostly because she knew the anime would overtake the manga and the anime wouldn't have enough time to keep up). And that's all we'll say on the subject.
Quasi-example: the Licensed Game, Fullmetal Alchemist and the Broken Angel, was released in the US just two and a half months after the anime's [adult swim] premiere, but was localized before the dubbing of the anime began; thus, all of the US voice actors were cast for and recorded the game before starting on the first episode.
Broken Angel also played this straight with Alex Louis Armstrong, as the game featured him a full month before the episode with his first appearance in the anime aired on U.S. television.
Overtook the Manga: A somewhat unusual case, in which the creator of the manga specifically asked the people making the anime to do this, since the manga was nowhere near being completed at the time the anime came out.
Hoho and Hohopapa for Hohenheim, Scarbro for Scar's brother, Sexyhobo/Gar for Scar (no, really!), Shinri-kun or Truth-kun for the guardian of the Doors of Truth, Greedling or GreedLin for Greed once he takes over Lin/Ling's body (which is used by Ed as a Shout-Out to the fanbase at one point), etc.
Also Bob the Blob/Proto-Father for Father's original form, Mr. Monopoly, Colonel Clean (a.k.a. Sparkleman), Palm Tree, Shota McShadowrape, Ninaxander, the Pimp Suit, Fetus!Envy, Godfather...