It was announced that 21,000 people rode the new tram link on Saturday — a figure which was much larger than anticipated.
The warm weather also played its part in attracting bumper crowds, with many queuing up to catch the first service at 5am.
And with so many people looking to sample the experience, tram bosses had to call in extra staff to deal with the demand.
Some people also reported problems with ticket machines while a couple of trams suffered small technical faults.
Tom Norris, director and general manager of Edinburgh Trams, said the issues were largely due to such a massive influx of custom.
He added: "It was never going to be completely plain sailing and we took measures early on in the day to keep things moving as smoothly as possible.
"We recognise that some pas-sengers had longer waits than will normally be the case but this was mainly because of the huge popularity of the new service and because we're bedding things in.
"There was a point when demand for tickets reached extremely high levels and this meant we could not sell tickets fast enough. A teething issue with two ticket machines com-pounded things."
Customers at the Haymarket and York Place stations were left frustrated as several ticket machines failed to issue passes.
Elsewhere, there were minor signalling faults on the line, while two trams had to be withdrawn and replaced due to problems with CCTV and electrical systems.
Another tram had problems with its door-release mechanism, leaving passengers unable to alight for several minutes.
The network is being run by the Transport for Edinburgh (TfE) body which is controlled by Edinburgh City Council.
A TfE spokesman said: "The sunny day encouraged a lot more people to come out. It was great to see the enthusiasm.
"We did have some issues with some machines, and have done work on the equipment and are keeping an eye on it."