The spell
So the first spell (that goes wrong), he just wants everyone to forget that Peter parker is Spiderman, and then he keeps adding conditions (except for my girl friend, except for May, ...).
I have an idea. If Dr. Strange refused to make exceptions, Spiderman could go to the people, de-suit and say "I am Peter Parker". Then Dr. Strange would not have to make any exceptions.
This next part may be spoiler.
I think the spell at the end was stronger. He wanted everyone to forget they knew Peter Parker. But did they still remember all the stuff that happened with spiderman?