Foreign nationals were housed in the facility near Heathrow Airport on the western outskirts of London in some cases for as long as four years, the government probe said.
Inspectors visiting Harmondsworth centre found that planned removals of immigrants had consistently failed to materialise due to last-minute legal challenges or a lack of travel documents.
The report, conducted by the government's Inspectorate of Prisons, also concluded that some detentions were delayed because of failings by the Home Office, the British interior ministry.
Publishing the probe, chief inspector of prisons Peter Clarke said: "The continuing lack of a time limit on detention meant that some men had been held for excessively long periods."
He added: "For the third consecutive inspection, we found considerable failings in the areas of safety and respect."
The report stated that physical conditions at the centre had improved but many areas were dirty, bedbugs were "endemic" and there were infestations of mice in some places.
Harmondsworth is the largest detention site of its kind in Europe, holding up to 676 male detainees.
It and similar sites are used to house foreign nationals, including overseas offenders and asylum seekers either while their cases are decided or prior to their removal from Britain.