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The test question is "What would you look for - - -?

Normally I'd look at the last thing that was changed or touched. In this case it seems that nothing changed. All sights were taken, and checked, before the interruption. The three large errors happened under the same apparent condition as the good sights. 

What COULD have changed? You could have passed local noon at the same time as the errors started but this is unlikely. I assume that you reset the reading and approached from the same direction for each shot to be getting those first precise readings. If not, a direction change on the rack would ( could) give an error but I wouldn't think it would be this large. This would be easy to check.

Next would be a search for factors with numbers that matched the error. I don't think any loose parts would give such a repeatable error. I don't think any atmospheric conditions changed in one or two minutes. GHA in late August changes about 5'/day. Declination in late August changes  21-22'/day. Humm. Could you have had to reboot the phone App and entered the wrong day by one?

Regards, Noell