Corn products of concern for fall cover crops are atrazine or simazine, particularly for legumes, brassicas, or annual ryegrass. Both persist longer on higher pH soils (pH 7 or greater) or soils recently limed, so watch surface pH in particular.
Herbicides with shorter half-lives (time required for 50% of the active ingredient to dissipate) are always less of a concern. In addition, species sensitivity can play a role if only a small amount of residue is necessary to cause injury.
This past summer, Curran and Lingenfelter did a demonstration at the Landisville research farm using a log sprayer and herbicide rate to simulate herbicide half-life. Cover crops were seeded and herbicides applied in mid-May. The estimated half-life for atrazine is 60 days.
In that demonstration, the sorghum-sudangrass was mostly unaffected. All the other cover crop stands were still reduced at the 1/4X rate (0.375 pounds of atrazine per acre) which would be equivalent to two half-lives or 120 days with some species still being affected at 1/16X (0.094 pound acre) which would in theory be equivalent to 240 days or 8 months after application. Alfalfa and crimson clover were particularly sensitive to atrazine with a 60% reduction in stand even at the lowest rate.
So, look at what herbicide programs you're using and the potential for carryover injury to fall cover crops before seeding something this fall.