Greg, NAD 27 versus the more standard 1983-1984 datums will build some problems. Typically, the original recorder might have done a good job, but then they used the wrong datum, or they reported no datum at all. That is about the amount of discrepancy that you get off mismatched datums. In some terrain, that is enough that you would recognize it and compensate. In some other terrain, you might not recognize it until you were already in trouble.
Also, if your GPS receiver is way down in the bottom of a canyon where view of the satellites is limited, it has an impact on position accuracy. If you were up on the rim where the view is virtually unlimited, it is likely much more accurate. Also, before I start into any serious navigation, I let my GPS receiver "soak up" fresh satellite ephemeris data immediately beforehand. That just lets the receiver do its very best. If you don't get fresh ephemeris data, it might have less position accuracy. But, you don't know what the original recorder did to get his data.
Around the western U.S., I have found plenty of places where the printed maps have position accuracy problems. I have found plenty of places in a GPS map database that have problems, and I have seen rare GPS receiver "blunders." Although TOPO! tends to be very good, it is not 100% perfect, either.