Are you certain that the weeds in their yard are on the list of noxious weeds in your area? If not, you may not like them, but they're entitled to do (or not do) what they like on their own property, as long as it's not posing a health or safety hazard to anyone else.

Make sure your neighbor actually has items on the list before you call it in. If you haven't already read up on your local noxious weeds agency, do so before calling in. Depending on where you are, different agencies handle this kind of situation differently. And also, with Covid-19 going on, there are a lot of agencies that have temporarily suspended services, or have limited services at this time.

Unless there's local ordinances, your neighbor might not have to keep the flowerbeds as neat as you would like, nor be required to remove bushes if they aren't a hazard. Does your area have an ordinance about keeping the lawn mowed?

In general though, no, I would not start finding agencies to report a neighbor to because of their messy flowerbeds. I would just keep tending to my own.

Bookwoman and Beesneeds, thank you for your thoughts. Yes, from a distance it looks like at least 2 types would be on the noxious list. Normally, I would not bother if there were an average amount of weeds and they tended to them every so often, but they never touch them, so they keep getting worse. The worst area of weeds is sort of near our outside entertainment (deck, play set, etc), and I read that mice and other rodents and bugs can be attracted to areas with a lot of weeds. I don't really care about the dead bushes that I mentioned given the whole situation, but just wanted to explain about the overall appearance. One of the noxious weeds is wild grape leaves. In another area of the property, these wild grape leaves are growing through a tall shrub in one of their flower beds, but one of the single vines keeps growing toward our property line and it's getting fairly close. We do have an ordinance about mowing, but they've hired a service for that, so we have no issues there. I don't think I will bother with anything for the reasons you mentioned, but if it does start interfering with our property I will consider reporting the issue. Thank you both!

Is it true that you are sure that the weeds in their yard are on the rundown of toxic weeds in your general vicinity? If not, you dislike them, however they're qualified for do (or not do) what they like on their own property, as long as it's not representing a wellbeing or security risk to any other individual.