John Leguizamo plays both the Genie of the Lamp and the Genie of the Ring.
The miniseries has an And You Were There theme where Dougray Scott plays Sharyhar and Amin the beggar, James Frain plays Schahzenan and Sultan Harun Al-Rashid and Jim Carter plays Ja'Far and the Harun Al-Rashid's advisor. Pik-Sen Lim plays Aladdin's mother and a woman shown in the harem, while Ayesha Dharker plays the demon's wife and another harem girl.
Subverted with Mili Avital, who plays Scheherezade. It looks like she's going to play Morgiana too, but the Sultan notes that Morgiana sounds like an Author Avatar - and Scheherezade immediately insists she isn't. She's then switched to be played by Amira Casar.
Fake Brit: Scottish actor Dougray Scot puts on an English accent to play the Sultan.
Fake Nationality: The Chinese Princess Zubaida is played by Vanessa Mae, who is British-born but whose family are from Singapore. Elsewhere it's mostly averted. While the cast may not be the exact nationalities of their characters, most of them have the corresponding heritage at least. Rufus Sewell, Jim Carter and Dougray Scott are ethnically British, but look dark enough to pass for characters who lived during "Arabian Nights" Days.
Rufus Sewell, normally typecast as slimy villains, gets to play the gentle and bumbling Ali Baba.
James Callis also usually plays vain, narcissistic characters. Here he plays the heroic Prince Ahmed. But of course this was his first role, before his type had been formed yet.
Likewise for Andy Serkis, who was not yet known for his Serkis Folk roles. Almost ironically, in a miniseries that features three such characters, he has a small role as Ali Baba's lazy younger brother Kasim.