A number of roads remained closed on Sunday, including the Ballysallagh Road and Crawfordsburn Road near Bangor, as the clean-up operations were taking place in other affected areas.
The Met Office has issued a weather warning for further heavy showers and possible flooding from Monday afternoon until 3pm on Tuesday.
“Frequent and heavy showers may cause flooding and disruption to travel,” the forecasting body said.
Road users have been warned to allow extra time for bus and train journeys, and to be wary of spray and flood water affecting road travel.
“Flooding of a few homes and businesses is likely,” the Met Office said.
On Sunday, the NI Trafficwatch online service said disruption was still being experienced in the north Down area.
It said; “Ballysallagh Road closed from A2 Belfast Road due to flooding at Bridge – and also at Crawfordsburn Rd approaching from the Craigantlet direction.”
In Co Armagh, NI Water staff attended a potentially serious flooding incident at Sturgan Brae/Camlough lake, where they provided sandbags to local residents, while other statutory agencies carried out an inspection of the banks of Camlough River.
On Saturday afternoon, the PSNI warned road users that the Portaferry Road, Kircubbin had been closed at the junction with Inishargey Road due to flooding.
Some heavy showers were expected overnight on Sunday, mainly affecting eastern areas, and scattered showers forecast for Monday morning.
However, the Met Office said the outlook for Northern Ireland from Tuesday to Thursday was heavy rain on Tuesday, spreading north on Tuesday night “followed by sunshine and showers on Wednesday. Windy with occasional rain on Thursday”.
In England, residents in the south west have been warned of “significant coastal flooding” this week. amid heavy rain and strong winds.
Some areas of Scotland have also been warned that fresh deluges of rain could pose a “danger to life” from flood water.