The AA survey is too unscientific to be really meaningful, as it relied on members of the AA volunteering to walk a local route of their own choosing for around 60 minutes, noting down 12 different types of road and footway defects.
Just 1,912 people took part across the UK - meaning Edinburgh roads were probably only looked at by a handful of people.
The Scotsman is right that Scotland is ranked worst for potholes, but they have chosen not to report that Scotland was ranked 5th out of 10 UK regions for the overall state of its roads.
Also worth pointing out that "Edinburgh" is the EH postcode region - which is effectively the whole of the Lothians and not just Edinburgh.
You can find the AA report at:
http://www.theaa.com/public_affairs/streetwatch/aa-streetwatch1-full-report.pdf
The most detailed survey of road condition is carried out by the Society of Chief Office of Transportation in Scotland (SCOTS). Results of this survey are available at:
http://www.scotland.gov.uk/Publications/2010/12/17120002/64
This is broken down by local authority area - Edinburgh not the worst.