You can use just about any solvent, such as alcohol, acetone, and the others for the same purpose. Water would also work, but you have grain raising and maybe weaker wood joints. There is a glue that responds to UV light, you could use it and then shine the light on the wood to see if any glue streaks remain. But the MS also reveals scratches and other wood imperfections ....and is probably as cheap as it gets for that use.
Rubbing alcohol might work, though it has a fairly high moisture content (as I understand it). But I was referring to denatured alcohol....I keep quite a bit around for use with shellac. Any of these solvents evaporate fairly quickly, MS is likely the slowest....but even on a cold day it should be dry enough within less than an hour. Many finishes are (like oil base varnish) are compatible with MS, so you can actually apply varnish right over a light wiping of MS. Don't try that with all the possible combinations, but in many (maybe most) situations it shouldn't be a problem.
The best thing to do is wash the excess glue off with a wet rag when you are building and not have the glue stain to worry about. It's been many years since I've had to deal with a glue stain so I don't test for it. If it happens I would touch up the spot with a touch up marker before I apply the finish.
In addition to finding sanding and glue marks wiping the wood surface with solvent will preview the look and color of the wood if you intend to finish the item with a clear finish.
While mineral spirits will work well and give you lots of time to look at the wood, it will also take a long time to evaporate. You need to wait for the mineral spirits to fully evaporate before continuing with your finishing. I prefer the denatured alcohol mentioned by others. It evaporates more quickly than MS allowing you to get back to work faster.
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