I suggest using Selleys 750ml Rapid Mould Killer Remover with a few drops of dishwashing liquid. I recommend using Mr Clean Handheld Iron Scrub Brush over the affected area and see if the blemish will wash away.
Continue brushing until the tile is clean and all the dirt has disappeared.
If spilled paint has dried on the tiles, I suggest using a Trojan Safety Scraper With 5 Blades. Carefully scrape the paint off the tile while being careful not to damage the surface of the tile. Your goal is to remove the paint to reveal the face of the tile. - EricL
I've recently started using 30 Seconds 1L Shower Cleaner and have found it really great. You don't need to scrub. Spray it on and leave it to do its work. You can then rinse it off later. - MitchellMc
We still swear by CLR Bathroom and Kitchen Cleaner. It sure does stink, but gee whiz, it cleans bright and shiny. We only have to do ours once a month. Tip: once finished in the shower, quickly rinse soapy residue off the glass. Cuts down cleaning time. - darylhewston