Poor weather, a sudden spate in materials donated and transport issues left the containers unemptied but the relevant companies were quick to get on the job as soon as they heard.
Jars with food sauces still in them, sour milk bottles, cardboard, soggy newspapers and rain-soaked clothes meet drivers and walkers entering the car park.
The council admits it is its responsibility to clean up any material left behind after the skips have been emptied - as long as they are non-recyclables which could have been lifted by Shanks Waste Management.
A spokewoman said: "Shanks are responsible for servicing the various containers under contract to the council to ensure they can continue to receive glass, textiles and paper only.
"If there was enough space the public should have put the materials into the containers. If not, Shanks should have arranged the servicing."
According to the spokeswoman Shanks should collect any recyclable waste lying around the containers but would not lift anything that was fly-tipped: "There has been some disruption to cleansing schedules and the servicing of recyclate receptacles due to the festive season and the extreme weather which may explain any outstanding removal of fly-tipped rubbish."
Austin Lees, of Shanks, said that complaints had been received at the start of the week.
He added: "We emptied the recycling containers as soon as we could get a lorry there. The containers are usually checked and, if necessary, emptied on a weekly basis. However, the poor weather recently and an influx of waste materials being deposited meant the containers were filling up much quicker than normal.
"We apologise for this and assure the public that we will continue to monitor the situation on w weekly basis."
And Michaela Crosthwaite, of Capability Scotland, said that as the car park was being dug up by council workmen for drainage, their lorry hadn't been able to reach clothing containers: She added: "We are very grateful for all donations and clear the bins every week. On this occasion, we struggled with access and it seems everyone has been having a clear-out as the bins filled up much faster than normal."