My wife walked across our lawn spraying Round up on various weeds. How long will the ugly yellow spots stay ?. Should I dig out the areas and reseed?
The ugly yellow spots are dead. Grass might fill in there eventually or weeds might, so if you want something pretty, reseeding is probably a good idea. The RoundUp packaging discourages using it that way, because of the results you describe. It says not to use it for spot treatment on lawns, not to spray it on anything you don’t want to kill, and that RoundUp will kill grass.
Now is still a good time to reseed in Michigan, if your do it this weekend. Make sure to keep the seeds moist for the next couple weeks.
You don’t use Round-up unless you want an Ultimate Solution Scorched Earth Policy (like back alley dandelions, for example), which you’ve probably figured out now. You want something like Killex for weeds in lawns. I would re-seed, after making sure the Roundup has been washed out; if you don’t re-seed with grass, things like dandelions and quack grass will fill in the spots for you.
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It is not necessary to “wash out” the Roundup. It is absorbed strictly through the leaves and has no soil activity. You can literally reseed at the same time you apply Roundup.
There are other “Weed and Grass” killers that DO have soil activity. In general these types will advertise “No regrowth for up to one year”. You need to be very careful where you use these types, as they are of the scorched earth variety.
Hmm, I thought I had read something about not re-seeding right after applying Round-Up. I must be thinking of a different herbicide. Maybe I just thought something that lethal to growing things would have residual activity. Thanks for the enlightenment. 
(I need some of one of those scorched earth varieties for a few spots around the yard.)