I feel your pain! I don't have wood slats though. I used to have a woman who would scream bloody murder when me or anyone above me over watered. Rude obscenities. She also reported me to our condo association. Once when sitting quietly outside reading, the person above me overwatered and it dripped directly on me so I politely called up. I got as far as "excuse me to the person above watering..." when the rude lady below me starting yelling threats to call the condo association. When she was done I responded that there was no need to be so rude. She shut up and has since moved. That said, I had old towels lined up by the edge of my balcony and was very careful watering. Plus I watered early in the morning and during the day when I was able to work from home...aka anytime when the nasty lady wasn't out.

Have you tried self watering tools? Most decent garden centers have them and Gardeners.com has an assortment--kinds that water when you're on vacation to smaller daily ones. They'll slow release so should help.

Don't the balconies get wet when it rains? What's to report? Is there a rule against plants on the balcony? Unless someone's sitting down there at the time, seems like a perfectly reasonable thing to do.

But practically, it's not as clean, there is some merit to the complaints. So if I had this issue, I would try to get the water to drip away so it just hits the ground, maybe with some of those rubber mats that go under a dish drainer. Kind of tilted, with 3 higher sides and a low edge for water to fall back into the sink.

Glad your nasty neighbor moved, Liz!

Oh Good Grief! I have a downstairs neighbor who yelled at me for MISTING my plants! I told her that her cigarette smoke comes up to my apartment...including inside because I have my windows open. I also talked to the apt complex manager about it & he told me that as long as it's not excessive, there shouldn't be a problem. Your neighbor sounds like a real charmer. I, too, feel your pain.

Maybe some plastic sheeting in the form of an old shower curtain?

Oh! I have a wooden plank floor. So this is what I do and what I like that is suggested above. I use a combination of pots with no drainage (this only works if you are an underwaterer by nature-- if not, then it quickly leads to rot and is not recommended), large saucers, and water during "off" times-- early in the morning most often, but sometimes mid-day.

I like the shower curtain suggestion. You could cover it with a rug of some sort. i happened to put down woven beach mats which catch any spills.

Yes, rain does come through I am sure. I do think it is a ridiculous complaint if not excessive.

Walmart and some of the BBSs have these cheap, very deep clear plastic saucers. You may consider them. i am not sure how deep your saucers are, but these are 2"+. It may be worth it if yours are more shallow.

Absolutely, it would be rude to not look first to see what is down there. And it's not necessary to make a big, wet mess watering plants. I use drip trays for plants on my wood porch because if I get the porch wet that often, it will not last as long.