Many maintenance jobs on the Piccadilly Line are more than three years overdue, according to leaked documents.
A report by contractor Tube Lines said the faults included split and rotten sleepers.
Tube maintenance workers voted to go on strike on Monday over jobs, pay and conditions.
The RMT union said the documents showed public safety was at risk. Tube Lines said its maintenance record was good.
The report, which was leaked to BBC London, outlines dozens of defective faults yet to be fixed.
It revealed at least three were still not fixed more than 1,400 days after being reported
The RMT union said the problem was caused by funding and staffing costs and blamed a recent derailment on late maintenance.
Spokesman Bob Crow said: "Due to the cutback in funding they are pushing back to the situation where it is becoming unsafe."
A Tube train with no passengers on board was derailed on the line in the early hours of 12 May.
The RMT said the incident may not have happened had the faults outlined in the documents been rectified.
A spokesman for Tube Lines said: "If you look at Tube Lines' record over the last few years, we have eliminated 4,000 safety related defects over three lines.
"That's tremendous progress."
Tube Lines' contract to maintain the lines is due to end by the end of June after being bought out by Transport for London.