The quaint ding-ding of tram bells has become an everyday sound in Edinburgh in recent weeks, as novice tram drivers practise navigating the vehicles through busy city streets.

It is a sound many of the capital's long-suffering residents thought they would never hear, so long have been the delays and so great the mismanagement of this project.

When the trams finally start carrying passengers tomorrow, more than three years later than first promised, residents are likely to feel a mixture of curiosity, excitement and sheer relief that they can finally put the fiasco of the building phase behind them. Natural as that sentiment is, however, there is still a strong case for a public inquiry into what went wrong with the project.

The benefits of such an inquiry are clear. It would not be an exercise primarily in apportioning blame, though identifying who took which decisions would come into it; it would be about learning lessons so that other local authorities and public bodies undertaking big infrastructure projects do not make the same mistakes.

The original plan was for trams to run from Edinburgh airport to the west of the city, past Haymarket, through the city centre and down through Leith to the waterfront at Newhaven, at a cost of £545m, to come into service in 2011. The reality is a much truncated network that stops at York Place, to the east end of Queen Street in the city centre, cost £776m and is only just opening now. Was the bitter conflict between the council's arm's-length Transport Initiative Edinburgh (TIE), and the contractors' consortium, avoidable; how well run was TIE; can anything be learned from the way the council's legal agreements with the contractors were drawn up; how effective was council oversight of the project; should the Scottish Government have offered more assistance with the project and taken a bigger role in overseeing it at an earlier stage; and are local authorities appropriate bodies to commission and oversee such huge infrastructure projects if they have no previous experience of doing so? These questions need to be answered.

The latest push for an inquiry, involving an online public campaign and petition, comes as it has emerged that Edinburgh City Council could consider legal action against TIE - a move which, if taken, could delay any public inquiry by years. The Scottish Government is supportive of an inquiry, even though few of the players involved, whether councillors, council officials, contractors, Government ministers or officials, are likely to emerge from it smelling of roses.

Whether ministers will maintain their backing for an inquiry in the face of protracted further delay is another question. But the prospect that this embarrassing mess could pass by in a fug of confusion, claim and counter-claim, without any clear picture emerging of what went wrong, is depressing. Public infrastructure projects will always be subject to delays and overspends if efforts are not made to make them more efficient, a process that has to begin with learning the lessons of past failures.