a broken-down fence.
a creaky shack.
a decrepit bus...its seats held together with friction tape.
a flea-bitten sofa.
a ramshackle old pier.
a run-down neighborhood.
a street of bedraggled tenements.
a tumble-down shack.
a woebegone old shack.
derelict (or delinquent) in his duty.
neglectful of his duties.
remiss of you not to pay your bills.
weed-grown yard of an abandoned farmhouse.