General terms:
* Invasiveness: invasive plant, invasive species, pest plant
* Harmfulness: harmful weed, damaging weed, destructive plant
* Unwantedness: unwanted plant, nuisance plant, troublesome weed
More specific terms:
* Poisonous: poisonous plant, toxic weed
* Allergenic: allergenic plant
* Aggressive: aggressive weed, rampant weed
* Harmful to animals: livestock poison plant, toxic to pets
* Impact on environment: ecological threat, ecosystem disruptor
Informal terms:
* Weed: (can sometimes be enough, depending on context)
* Pest: (can be used when focusing on the damage)
* Scourge: (stronger term, implies a serious problem)
The best word to use will depend on the specific situation and the desired impact.