The New Mexico police officer has a Mexican flag (without the crest) on her uniform.

Does this mean that the Mexicans invaded and annexed New Mexico?

(it actually more closely resembles the Italian flag but I'll go with the more realistic option)

I can only assume it was a mistake on the part of the Zygon

more likely a silly mistake by the production team - like having electric eels in viking Europe and having reel to reel tape recorders in 1941 England (Even though the allies only found out about them at the end of WW2