There is probably no need to contact the BAR though you always have the right reserved. Trouble Code P1774 indicates your Mini's rear wheel speed sensor lost its signal, and trouble code P1775 indicates the right rear wheel speed sensor lost its signal as well. Both more than likely triggered during the dynamometer portion of the smog check inspection; while the front wheels are turning and the rear wheels are stationary. During this time, as far as the ABS system knows, the rear wheel sensors have lost their signals.
After a computer reset and driving your Mini Cooper for a few miles everything should return to normal, as apparently they have; and you've passed the smog check. Should the check engine light return in the near future for the same trouble codes (P1774 & P1775) we'd recommend inspecting the rear wheel speed sensors for possible debris build-up. Since these trouble codes where triggered during the smog check and smog check machine failure we can assume the trouble codes were temporary and not related to any physical problem with your Mini Cooper.