I played Abe's Oddysee a few times when I was a child, decades ago, and been playing it from time to time. It's one of those special videogames that contain unique feeling and atmosphere and are difficult to forget, with amazing attention to detail and craftsmanship.
This new version does a better-than-average job and manages to keep most of the spirit and essence of the cinematic and dark original. Some is lost, though, or transformed, as it's impossible to do a remake with new technologies (from 2D to 3D) without losing something. But I believe fans of the original will be satisfied with this version, unless they are too purist, as it manages to keep most of the original soul.
The only thing I didn't like that much was the song for the credits. I think it breaks apart the tone, feeling and personality of the videogame. A “standard” song shouldn't be used, but an original, ambiental/folk (excuse me, I don't know the exact genre) music like the original instead.
Nonetheless, this remake is a respectful, lovely and carefully-made remake of a unique classic, and I recommend it.
I didn't experience any bug on 2.1.0.3, even repeatedly using the quicksave. Subtitles were a bit off-sync in some particular moments, but nothing major.