I left it but did improve it slightly. It was in a basement so it ended looking a little rustic!
Bad news on the sealant. It does need to be reapplied periodically (I'm talking years here) although I believe that areas of little wear will fare better. Pour a little water on the slate and see what happens; if the water sits on top the sealant is still working! If not, the time it takes to get absorbed will be an indication of how well it's working.
Paint droplets aren't difficult to remove. Be patient, use a chisel but be gentle as the slate will 'scratch' . Use wire wool too but again I have found it too abrasive, so be gentle. Ignore the sanding suggestion made earlier (could have been another forum, mind) since it's ridiculous. White spirit helps, but wipe off quickly esp. If sealant ain't working. However, where watery paint has dried creating a sort of film - I just dont' know. I wonder whether paint remover would work but I wouldnt try it, to be honest with you as it will damage the slate. A good possibility I think is white spirit, a green pan/dish scrubber and elbow grease although take care because the green scrubber could afect the tiles adveresly.
What I WOULD do is to try everything on an inconspicuous area e.g. How hard to scrub with wire wool, how much pressure you can get away with using a chisel etc. because slate is not all the same and yours may be better than mine.
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