Corrected entry: Throughout the series of Angel, they have episodes with scenes of his past where he is cleaned up and acting like he does in present day. For example in season 2 episode 2 "Are You Now Or Have You Ever Been" he seems like normal Angel only in the past. Same situation with season 5 episode 13 "Why We Fight". But on an episode of Buffy the Vampire Slayer season 2 episode number 21 "Becoming part 1" there is a flashback of Angel in 1996, way after those episodes of Angel and he is a complete mess living off of rats and we are led to believe he has been this way ever since he got his soul back. So he couldn't have been as sane and well kept and living off human medical blood as he was depicted in those Angel episodes.
Corrected entry: In 'Orpheus', Willow mentions that the restoration of the soul was the first spell she did. Back in season 2 of BTVS, however, she did several spells before that, for example revoking Angel's invitations in 'Passion' or her attempted exorcism in 'I Only Have Eyes For You'.
Correction: Williow actually states that re-ensouling Angel is one of the first spells she learned, not the first spell she did.
Corrected entry: In the Buffy episode 'The Prom' Angel mentions that he never drinks coffee as the caffeine makes him jittery, yet he drinks coffee in quite a few Angel episodes. It's unlikely a 243-year-old would change his habits in the space of a few months.
Correction: Perhaps sometime after The Prom, Angel discovers decaf. It's possible, especially for someone so old who didn't seem to "get" Buffy (or women in general) 90% of the time, to not be up to date on coffee. He makes other changes - he takes up smoking in the fifties flashbacks of season two, gives up smoking for the entire time we know him prior to halfway through season two, takes up smoking, and then gives it up...again.
Corrected entry: Cordelia says in the episode 'Awakening' that she has encountered the real Angelus when he changed in Sunnydale, but during the episodes after Angelus changed in season 2 of Buffy the Vampire Slayer she never actually saw him, just heard about him.
Correction: She further clarifies in Awakenings that she saw everything he EVER did (as Angelus) in "virtual wide screen sense surround sound during my tenure in floatyville". She saw firsthand what he was like. Also, on Buffy, Cordelia spoke often of the badness of Angelus. Cordelia did actually meet Angelus in the BTVS season two episode "Killed By Death".
Correction: Actually the writers/producers of episodes like this have often said that they wrote in back stories like the ones mentioned specifically because they didn't believe that Angel had been a complete mess ever since being cursed. The various ways he is seen living in the time since show his struggles with trying to work out where he fits into human society. Also, he's hardly acting like he is in the present day in Are You Now Or Have You Ever Been when he allows the paranoia demon to eat everyone in the hotel.