So using your previous example that the last fix was obtained at 16:23GMT (roughly 400NM out). If FN assumed a 15NM error when the fix was obtained, if he was within the average error margin would he have simply ignored any difference between the fix and his calculated DR position or would he always use this new fix and assume the DR calculation was incorrect?

The standard navigation technique is to start a new DR plot from each new fix. In flight navigation you also plot the DR position brought forward from the prior fix for the same time as the new fix and the difference from the DR to the new fix tells you what the wind is so that you can correct for it. Here is a

link to an example of how this is all done. We can also see from Noonan's Hawaii flight chart that he used this standard method.

Assuming that his last fix could at 16:23GMT could have potentially had an error of 15NM, do you then add this value to the DR error around Howland (10% of 400 = 40NM) so that you have a total potential error of 55NM?

The uncertainty in the previous fix is carried forward with the DR. The DR can never be more accurate than the fix it started from. With a 15 NM uncertainty you can draw a circle of 15 NM radius around the fix. You expect to be near the center of the circle but you accept the possibility that you may be near the edge. If you then DR one mile that circle isn't going to get any smaller. So you do add the original fix uncertainty to the additional uncertainty caused by the DR leg, one mile for each ten miles on the DR leg so after DRing for 400 nautical miles the uncertainty in the DR position would be 55 NM and you would allow for this in planning the point to intercept the LOP and for searching along the LOP.

For the sake of argument let's say he did find a substantial error at 16:32GMT, say 30NM South of the line at 400NM out would he have computed a correction back to the flight line or would he have just computed a new flight line to Howland? When do you switch over from making your way back to a flight line and computing a new course to your destination?

There is nothing magic or important about the original planning course line you drew on the chart, there is no reason to try to get back on it. At each fix you just aim for the destination from that point since this always shorter than trying to get back on the original course line. We can see that this was Noonan's method from his chart for the Oakland to Hawaii flight.

Flying over land it may be important to get back on the original course line if, for instance, the original course approaches the destination down the center of a valley and if approaching from a different direction may cause to smack into a mountain. There are no mountains in the middle of the ocean.

gl