Can very dilute acids exposed to air become more concentrated as water evaporates? If a very minute quantity spilled acid (e.g. $\ce{H2SO4}$, though the question would apply to other acids as well) is cleaned up with water (e.g. yielding a $0.0001~\mathrm{M}$ solution), and some of the water (dilute acid solution) is left behind, will the resulting solution become more concentrated as the water evaporates?  Would there be any danger that a drop of an initially-harmless concentration might become a visually-unnoticeable quantity of acid that was strong enough to pose a contact hazard?  Would wiping an area down with a moderately-dilute solution of a weak base such as sodium bicarbonate be an appropriate safety precaution, or would it be unnecessary if any acid droplets that might exist on a surface have been thoroughly diluted?
Sulfuric acid (and other acids) can be concentrated through evaporation of water.  It would be a good idea to wash the surface down with dilute, basic solution.  That said, if I'm reading your post correctly, your droplets are already 0.1M.  That is still a strong acid and care should be taken in its clean up.  I was once working with a 0.01M solution of sulfuric acid and when cleaning the flask a few drops of the dilute solution splattered onto my foot, I didn't even notice it at the time.  An hour or so later my foot started to burn.  When I looked, my sock was gone in the affected area.  If you're dealing with anything more than drop or two use a spill kit and let someone know what you are doing.