What's the best way to wash uneven floors?

You have a few different options here:

- First, with a tile floor, if it's lightly colored, you're aware that a lot of stains and messes are pretty visible. So, you're going to be doing a lot of on-the-spot cleaning - or, at least, you should be. Buy some Clorox bleach wipes. They're the easiest way to handle those one-time clean-up jobs.

- A Swiffer Wet-Jet is fairly inexpensive, and will do exactly what you're hoping - it "grabs" most of the stuff you're trying to sweep away. An old-fashioned sponge mop tends to collect and store bacteria and smells inside of the spongy part - and it sounds like the one you own is probably past its prime. Upgrade to the Wet-Jet. Just make sure to pick up any carpeting/rugs, move any furniture out of the way, and go to town.

- You can still use a broom now and then for a quick clean. Just make sure to clear as much space as you can, and sweep any debris to the center of the room. The type of broom might be your problem - if the broom bristles are too stiff, they're not really going to "push" anything in the direction you want to go. A flexible group of bristles attack the grooves between the tiles, and move them towards the debris pile. Additionally, super stiff or hard bristles can just mark up cheap/aged/delicate tiles. So, once you have a decent waste pile in the center of the room, it's actually easier to use a hand-held vacuum (or an attachment for a standard vacuum) for removal.

- For hard to reach areas in corners or behind furniture, try using a lint roller. The sticky sheets will grab any dirt that you can't reach. You can also go the MacGyver route, and use a broom handle for really tough spots, like behind the fridge. Just use some duct tape, and attach the lint roller to the end of the broom handle. It might sound goofy, but then, you'll also be able to get to the ceiling, and other places your arms can't reach.

Use a big brush with strong plastic bristles, then mix powdered soap in a pail with some water. change the soap mix once in a while. To finish it, wash the soap off the floor with clean water using large pieces of cotton cloth, not just one. The dirt will be absorbeb by the cloth and you have to use a new one., Use the mop last.