Would the gestational age of 12wks+4days @62mm be off by 1 week since ultrasounds have a margin of error of 1 week in the first trimester?

Estimates. Determination of gestational age is based on estimates determined by the last menstrual period and ultrasound. There is a margin of error with ultrasound, but that does not mean that the gestational age is necessarily different by a week. It means that the ultrasound estimate is 12w4d with a very high likelihood that the actual age is between 11+ to 13+ weeks.
Probaby not but... No test is perfect and fetuses have variable sizes. The results mean the gestational age might be anywhere between 11 wks + 4 days and 13 wks + 4 days, with 12 wks + 4days the most likely. If you know the dates you most likely conceived (about 15 days after your last period began) this would help you better know how far along you are.
Usually +_/- 5-6 day. Gestational age charts are based on averages, as 6 lb. Or 8 lb. Baby can be normal at birth. Dating is based on first day of bleeding of your last menstrual period. The +/- means there is 95% chance that the gestational age is x weeks y days +/- 5 days.