"Please help me to order a coffee."
”请帮我点一杯咖啡“ Why is this incorrect? It says "...a coffee," so shouldn't I use 一杯 to specify that?
Yes, your sentence is correct as well as your reasoning.
Without 一杯, the sentence is general, which turns out to be "Please order me coffee".
With 一杯, the sentence identifies "a coffee/a cup of coffee" as the object.
Because you are saying ONE COFFEE, with the correct sentence, you are buying coffee, in packs, or two cups,or whatever.