Brazilian Peppertree
Earleaf Acacia is a really bad one- even worse than peppertree.
Any of the native exotic vines- that's why fires are good because they burn all that crap out.
Queen palm- drops 1000's of seeds and they have high germination rates and grow quickly.
Probably some grasses and sedges- but they all get mowed.
When I lived in Santa Monica, there was a Brazilian Peppertree on public property about 10 yards from my garden. Never-ending suckers coming up all over the place, which were impossible to eradicate.
As for here in Merida, I have issues with Hoja Santa (Mexican Pepperleaf), which I naively planted as part of my kitchen garden (the leaves are used in Oaxacan cooking) and is spreading underground like wildfire and popping up everywhere. Thankfully the chickens like it so I let them out to peck on the shoots.
Also, and surprisingly as it is a protected species in Mexico, is the Chit Palm (aka Florida Thatch Palm [Thrinax radiata]). I believe it is suffering from habitat loss, but I have several mature palms in my garden, and the fruit and seeds are super abundant and sprout everywhere. My lawn and planters are full of sprouted Chits and I am forever pulling them up. Speaking from my experience with the seeds, it wouldn't take much to get this palm re-populated in any area it has been lost from.
At the moment, no real issues with invasive animals, birds, or insects in my area other than African Honey Bees which are out-competing the very vital local Melipona bees.