I've made a LOT of planting mistakes. However three in particular come to mind
1. Chinese Lanterns (Physalis alkekengi). One of the many plants we put in to brighten up the various parts of our yard. What we never knew until it happened was how FAST the stuff propigates, both from birds eating the fruits in the middle of the lanterns and pooping out the seeds and from runners, and by extension, how FAR those runners can go. It took us YEARS to get rid of them.
2. Blackberries. On our property Japanese wineberries (Rubus phoenicolasius) are native (well, are naturalized). The produce well enough, but after a while we got a little bored with the monotony and though adding a few other bramble fruits would provide a little diversity. BIG mistake. That is, the idea may not be such a mistake but we picked the absolutely WRONG strain of blackberry from the nursey. Leggy, spread canes all over the place, prduced nearly NO fruit and what little it did produce was small, seedy and sour. Again, took us AGES to get it all out, and even now we get the odd cane showing up from time to time. Though whether these are leftovers from our own blackberries is unclear. They could also be leftovers from the wild bank of berries that used to exists in a hollow on our neighbor's property (until the area got basically razed to make another house). That one was much the same sort as ours; the berries, while more numerous than ours, were also not worth the picking or eating. (There was a tiny blackberry cane that I found one year behind our neighbors property one year that WOULD have been worth bringing onto our property, as it made excellent large berries (well berry, when I found it, it was so small it had only made 1) but I've never been able to find that one again.
3. Senna obtusifolia- This one might not count as we never "planted it", at least, not on purpose. But as a result of all those seed searches I do, I often toss large amounts of legume leftovers out on the lawn and the mulch pile, for the birds to eat and or to rot into mulch. Because of this, were pretty used to finding little patches of volunteer legume plants popping up in odd places all over our property. Mostly these are at best a minor concern. Most modern legumes are bred to soak swell and grow as soon as they are rained on, so nearly all seed thown the birds don't eat either sprouts (and gets mown) or rots (and stops being a concern). And plants that live so long they can actually reproduce without intervention are rare (and those that do tend to be so obvios I can see them and pick any seed they make before it hits the ground). But the senna is another matter. It can't QUITE finish it's reproductive cycle up here (I'm actually only about 10-15 miles from your weekday residence, NYboy) But the amount of seed that can hibernate in the ground for years and then pop up makes that all but irrelevant. Every year we get a good smattering of little senna plants all over the place. Since I stopped actively throwing senna seed out we get a lot less of the real titans (one of the years I was doing that, we would up with some senna plants that were big enough to count as small trees) but there are always some still, including a few that try to make flowers and reproduce. The flowers ARE sort of pretty (look a little like buttercups) but on the whole I am not a big fan of a lot of senna plants since they STINK when you crush or cut them.
Those are the main three I can think of. I suppose I could include things like the hellweed and the grasp vine (don't bother looking those up, they are my personal nicknames for the plants since I don't know what they actually are) but those have only been problems for a single year, and never extended furter than where I planted them. I'll write a bit about them, but only if someone asks me to.
