Being Dario Argento's first film and a breakthrough in the conception of the 'giallo' murder-mystery genre, "The Bird with the Crystal Plumage" is definatly deserving of it's acclaim. It's innovative status should be taken into consideration since this very same premise was used (particularly by Argento) for numerous other such films back in the day.
An American writer living in Italy with his hot girlfriend witnesses an attempted murder through the window of a art gallery after closing. He is not able to see the attacker's face before he flees, though he is determined to assist cops in the mysterious killer's search while more young women are brutalized...
If you've seen "Deep Red" or "Four Flies on Grey Velvet", you'll recognize a bit of a 'trend' in the 'giallo' storyline, though I'll give props to "The Bird with the Crystal Plumage" not taking the overly convoluted route that many comparable 'giallo' flicks took on and this one doesn't drag on or get too long winded. Not a lot of gore shown upfront, though there's a straight razor slashing and an implied vag-stab (obviously cut from the initial PG rated version). The stuttering pimp and cat eating painter characters were amusing and the big end reveal was clever.
Despite, personally, being a bit burned out on these types of murder-mystery 'giallos' over the years, "The Bird with the Crystal Plumage" is worth a look for hard-core Argento fans and 'giallo' enthusiasts alike.