I use is most days, and yes in places it is very narrow and has tree roots under the tarmac. The stretch which runs parallel to the off ramp on the A90 south bound to meet the Kirkliston road is the worst stretch. The path either side of it is ok but could be improved. The worst stretch I pointed out above is terrible at night in winter as when riding to Fife or South Queensferry, has cyclists on the same side as oncoming vehicles which serverly limits vision especially at the stretch where the path is sunk so that vehicles are actually at eye level.
Further out the path has been made wider and there are threads on here with photos.
There are alternatives which mean riding on the road, including Standingstane road and left onto the road between Kirkliston and Craigiehall/Cramond Brig which does have some fast moving traffic at rush hour(s).
Another alternative is to ride through Dalmeny estate which is tarmac the whole way but drops to sea level and has a steep rise in either direction which can be off putting.
A particularly bad stretch is up from Ferry Toll on the path to the bridge. Both pedestrians and cycles have to share a 2m wide path with cycles in both directions as well as pedestrians who are walking up to cross the bridge.
Helen Eadie is a very great supporter of cycling and I ride with her son in law (who wrote large parts of her speech and is standing as a councilor in Dalgety Bay, Hillend and Inverkeithing), in the past Helen was responsible for pushing for cycle paths through our consituency and the Fife Coastal path.