Concerns about the safety of railings on the building's upper floors then prompted Glasgow City Council to delay awarding the five licences required when it met on Wednesday.
The attraction had to turn people away just 24 hours after it opened because of a delay in securing a public entertainment licence.
The centre also had to address safety questions raised by Glasgow City Council before it got the all clear.
But the project finally received its necessary permits on Friday, allowing the centre to open its doors for good on Saturday.
An estimated 500 people had gone through the doors of the centre, which has 300 hands-on displays, by 1200 BST.
Spokesman David Grimmer said: "Everything is going smoothly and people are inside learning about science and the world in the way the centre intended.
"Hopefully we have put the problems behind us and we can get ready for the official opening by the Queen on Thursday."
The titanium-clad visitor attraction was forced to close just a day after its unofficial opening last week when it emerged that the Science Mall did not have a vital permit.
An estimated 1,000 visitors arrived for the attraction's first day - but could not be charged an entrance fee.
Concerns about the safety of railings on the building's upper floors then prompted
Glasgow City Council to delay awarding the five licences required when it met on Wednesday.
However, councillors awarded four of the licences on Friday after hearing that managers had installed clear plastic screens to make the railings safe for young children.
Christine Devine, convener of the licensing sub-committee, said: "All the safety issues raised by the city council have now been addressed and we are happy to endorse the Glasgow Science Centre as one of Scotland's foremost visitor attractions."
The decision on the fifth licence, which does not directly impinge on the Science Mall's opening, has been delayed until August.
The centre houses hundreds of interactive exhibits including light beams, mirrors, optical illusions, audio and computer displays and water tanks.
Revolving tower
The centre's mall and the adjacent Imax theatre, which opened last October, have been hailed as the UK's first titanium-clad buildings.
The final part of the Glasgow Science Centre site, the world's first revolving tower, is due to open to the public next week.
It is still facing an inspection before its public entertainment licence can be granted.
But Mr Grimmer said: "No-one is anticipating any problems with the licence for the tower. It should be open to the public in time for the royal opening."