think a lot of people confuse Jimmy Page's supposed sloppiness with the improvised aspect of his live playing. When you make it up as you go along it is not always going to be clean and neat.
As he stated he Would Rather Live a day as a Lion than a Thousand as a Lamb.
Also, one of the features of many of Jimmy Pages solo's is the stuttering effect he produces before ripping into a long lead. This can be heard at the 3minute 09 second point of Prison Blues off of Outrider, and the 2minute 09 second point of I Can't Quit You Babe off of LZI.
This youtube link is a very good example of Pages technical skill.
This is White Summer/Black Mountain side from a T.V. appearance. Although highly improvised, it is very skillfully crafted and played as compared to the Led Zeppelin DVD version from Royal Albert Hall. To boot this version is played on a Gibson SJ-200 Jumbo acoustic making it considerably harder to perform especially at the speeds he's playing.
Granted the recording quality leaves alot to be desired