Outside of the very obvious removal of the beautiful bookended credits (this one still blows my mind) and the shortening of the scene when Billy and Garrett first meet (really odd decision IMO), here are some of the editing decisions that I find particularly troublesome in the 2005 edition as opposed to the Turner Preview edition:
Outhouse scene: The replacement of the shot of the bucking horses when Billy walks out to the outhouse with a shot of Billy walking through some pigs. While the shot of him walking through the pigs is a nicer image, the shot of the horses ties in well with the following shot of the horses in a much calmer state immediately after Billy exits the outhouse. The horse shots bookend the outhouse sequence well and it's great how they are frantic before Billy retrieves the gun in the outhouse but then calm down once he exits as if representing the calm before the storm.
Cockfighting scene: The cockfighting scene when the flurry of feathers transitions to the shot of the guy being rounded up by Garrett on his horse is far better in the complete Preview version than in the shortened Special Edition.
River scene: In the Turner Preview, there is a nice audio transition from the song being sung in the outpost scene to Garrett sitting on the bank as if the lyrics to the song are in his thoughts. In the 2005 Special Edition, while there is a nice additional shot setting the scene before we focus on Garrett, the cut from the preceding scene (now the one with Billy and Alias fending off Chisum's regulators) is abrupt. We also lose a final shot in that scene that focuses on Billy's face almost as if in slow-motion. It's a great shot that adds a quiet tranquility to the end of the scene that then transitions beautifully to the scene with Garrett cooking his food on the frying pan.
Brothel scene: In the Turner Preview version, the owner of the brothel/saloon knocks a glass over and this transitions beautifully into one of the prostitutes turning the hourglass over. In the Special Edition we lose this nice transition because the Ruthie Lee scene has been added before it. Instead we get a decent audio transition from the sound of the glass being knocked over to the sound of Ruthie Lee knocking on Garrett's door, but it is not as strong as the original.
I find the Turner version almost poetic in its editing and transitions; I personally feel the 2005 edition loses this.