Overwriting the actual story (Homer's version) with one's own version is an insult to the classic. Greek civilisation back then wasn't as just and equal as BBC would want it to be and this is their sad attempt to override that. Achilles and Zeus (even as fictional characters) were never imagined or portrayed to be black and no Indian kings had sent shiploads of silk in order to win Helen's hand in marriage (from what we know so far).
Hector wasn't such an imbecile as shown to be but was a respected figure across both the Trojan and Greek camps. Slight mention of Ajax. Odysseus is shown as cunning as ever and an attempt to evade the war is also shown in the same light but while this interesting act has been captured in the show, Achilles' attempt to escape the war is not even mentioned let alone be picturised.
However, certain crucial facts have been represented correctly in the show like how Paris was promised Helen or the story behind why he was abandoned in the first place etc etc. For this reason alone, the show isn't a complete disaster.
Just one word of advise to BBC, if you want to film such a classic, stick to Homer's version and include if you can any verified additions or subtractions made by experts in this field but kindly, refrain from filming your own leftist version of the Illiad. Nobody gives a damn about BBC's Illiad as reviews will show soon enough unless that's already happened. Leave classics be.
And were you seriously thinking people would fall in love with your version of Achilles and Hector after what Brad Pitt and Eric Bana portrayed them to be?