IMPORTANT NOTE: This was written several years ago. The logging roads are unlikely to disappear, but the condition of Caribou Valley Road varies from year to year.
There is a perfectly good trail to Mount Redington, however it is not described in the guide book nor shown on any current map. I am assuming that you have the new AMC map of the Rangeley-Stratton area, which shows Caribou Valley Road and the first logging road that branches off it. Alternately, you can use a TopoZone Map of the area.
Drive along Caribou Valley Road about 1.1 miles beyond the AT crossing, where you will find a wide area where you can park many cars. The condition of logging roads can change very fast, but in July 2001 Caribou Valley Road was quite drivable up to the AT crossing, and definitely drivable to the parking area. We had no problems with an SUV, and found a couple of sedans parked there.
There is a fork immediately after the parking area, not shown on the map. Take the left branch, which follows the river. In July 2001 it was marked by a cairn, but a good look at the map should make it clear that you want to follow the river. The road immediately crosses a tributary over a bridge that was in very bad condition, no cars had crossed it that day. Follow the road over a mile to a second fork, which is shown on the map. Take the right branch, the left branch immediately goes over a bridge. Continue through a logged bowl, and enjoy the raspberries in season! At the next fork take the right branch (again, shown on the map with dashed lines) and climb uphill. This is an older logging road, much rougher than the main Caribou Valley Road. Keep going up until you practically reach the ridgeline, you will find a very clear road branching off to the left, there are many cairns and an arrow made out of sticks to mark it. Towards the top of the road you will run into several cairns on the side of the road that do not signify anything, ignore them! They caused us some confusion.
Take the road that goes to the left (not shown on the map), and follow it. You will reach an obvious fork where a newer road goes up to your right, ignore it and continue straight ahead on the now grassy road (cairns and arrows mark it). It goes through an area of new growth spruce following a clear cut, once out of that area there is a trail going to the right, marked with heavy flagging. Follow the trail to the summit of Mt. Redington.
The description may seem complicated, but if you follow the directions you should never be in doubt as to where to go.