I have traded with a trainer or two that had stats that started out three star with one or two stats at max, then when the Pokemon came to me they dropped to zero to one star and became super weak. Anyone else having this trouble?
Yes, but thats just how trades work.
The IV floors for trades with different kinds of friends are:
Good Friends: 1/1/1
Great Friends: 2/2/2
Ultra Friends: 3/3/3
Best Friends: 5/5/5
Lucky Friends: 12/12/12
So its not advisible to trade away pokemon with good stats but the ones with bad stats.
That explains it. The only exception to that rule is lucky Pokemon. I used to get guaranteed lucky Pokemon from trading off my oldest Pokemon.