One morning last week I arrived at Mass during the Consecration and I wasn’t sure whether I could go to Communion. What is the rule on this during a weekday Mass?
You could have gone to Communion. The Church does not require participation in the Mass for reception of the Eucharist, so if you show up late it is perfectly fine to go to Communion. The only exception is for those who have already received the Eucharist that day—canon law does require participation in the Mass for a second reception.