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Did men pop their waste in here? (6)

Miss Bannister contains Dichlorodiphenyldichloroethylene. What a load of rubbish. (5)

MIN Bannister from the Goon Show

Dichlorodiphenyldichloroethylene Chambers has this listed as DDE

Dump central study (6)

Miscellaneous items discarded daily emitting noxious smells from tips (7)

For those not familiar with the Goons:

https://en.wikipedia.org/wiki/Henry_Crun_and_Minnie_Bannister

Mine shattered large cups buried here? (6)

DD in (MINE*)

Mind Ed making a mess (6)

Should have a '?'

Disorder from fringe elements in Miami disrupted election (6)

Outer letters

Disorder north of the border kept secret money for Henry (6)

hIDDEN (kept secret) M for H

Henry Percy perhaps…
https://en.wikipedia.org/wiki/Henry_Percy_(Hotspur)