Barry, The fruit of the poisonous tree doctrine prohibits evidence of a crime from being used if it was obtained by violating one's right to be free from an unlawful search and seizure (4th Amendment). The idea is not that the evidence isn't good or that it isn't probative as to guilt or innocent. This kind of evidence is often the best. The idea is by barring its use the police will be deterred from disregarding the Constitution.
IIRC, the biggest chink in the poisonous tree doctrine was a decison, perhaps it was Wolfe. I am not sure and the name isn't that important. The decision allowed the use of evidence although it was fruit of an improper search, but the police had acted in good faith. I beleive later cases have expanded on the good faith exception.
Here, I believe the court would find that the police acted in good faith since the city ordinance banned the carrying of a weapon, if they did not know that state law pre-empted it, and the weapons license appeared to be invalid. The birtdate was incorrect. Besides, the fruit of the poisonous tree only applies to the ban of evidence and what evidence does anyone seek to ban?