I'm not saying his run didn't interact with other comics, just that Alan Moore's Swamp Thing didn't make long lasting changes to very much, outside maybe to Swamp Thing. Its not really a comic where Alan Moore got a lot of freedom so much as it was a book about a D-list character that DC let Moore mess around with because it really didn't matter to them. He wasn't pushing limits with the book because DC didn't care enough about Swamp Thing to give Moore any real limits.
Actually, Len Wein, co-creator and then-editor of Swamp Thing, called upon Alan Moore, because he liked his work on "Miracleman". If DC didn't care enough for Swamp Thing, they would never have gone to the trouble of hiring a writer who lived in the UK (it was actually unheard of at the time, and without the help of the internet, it was no easy feat). You can bet, the character's co-creator cared very much about said character.
Also, Moore very much pushed the limits of what could be published in a comic book involved in the DC Universe, with quite mature themes. And it was so popular, that not only is it the seminal work on the character, not only did Moore create the "overrated" John Constantine for this book - who went on to star in more than 300 issues of comic books, as well as a movie and a (too) short-lived TV show, so popular was he - , but the whole Vertigo imprint is based on the success of Alan Moore's Swamp Thing.
You may not like the book (or John Constantine), but that might be because it wasn't a superhero book, and it never was. Swamp Thing is a fantasy horror character, same with John Constantine. You have every right to dislike the characters or the genre, but it's ridiculous to downplay the popularity and success of Moore, the book, and/or the character.
As for lasting effect on DC characters outside of Swamp Thing, well, no, the book had no lasting effect on DC characters outside of Swamp Thing (and John Constantine), if you define "lasting" as lasting more than a few years. But why would you expect it to have?! It was a book on Swamp Thing, not the JLA, or the Green Lantern Corps. Exactly how many lasting effects on Superman have there been in Detective Comics over the years?
Looking up what you said about Mento, I just saw that Moore is responsible for the terrible "Mento is an insane villain" thing, and he killed off Zatara and Sargon, all in Swamp Thing. That actually makes me really dislike Moore's Swamp Thing by association, well that and the fact that he introduced the most overrated (yet still B-list) character in DC comics with John Constantine. I like a lot of Moore's stuff, but his runs with DC heroes almost seem designed to drive me nuts. Outside of one good Superman story (For the Man Who Has Everything), Moore might be the only good writer whose original/non-hero stuff is better then his hero stuff.
Well, taste is always up to the individual. But there's no denying Moore had some influence on other DC works, in terms of characters, as well as on style.
Outside of Swamp Thing, Moore had very lasting effects on DC characters in the small number of stories he wrote in the DCU. He created the living planet Green Lantern Mogo, who was used decades later and was even featured in the animated "Green Lantern: Emerald Knights", he wrote the bookend for the pre-Crisis Superman in "Whatever happened to the Man of Tomorrow?", and his "Killing Joke" had a very lasting effect on Barbara Gordon.
You may not like his work from the 80s, which is fine, but the legacy of Alan Moore, both at DC (and Marvel, thanks to his "Captain Britain" stories) and with his original comics is irrefutable.
As for works by Alan Moore you might like, given your dislike for his darker stories from the 80s, maybe you should try his "Supreme" comics, which were one huge love letter to Superman. You might also enjoy his work with America's Best Comics, especially Tom Strong and Top10.