Audit Scotland said the £1.3 billion project was well executed and represented value for money, but its wider benefits had still to be shown.
Audit Scotland accepted there had been “prolonged adverse weather conditions during key stages of construction”, which put the opening back from December 2016 to last August.
However, it was subsequently revealed completion work would continue until next month and under-deck painting would go on until 2019.
Overnight lane closures since last November for the work have caused delays.
The watchdog said: “[Scottish Government agency] Transport Scotland could have managed the public’s expectations better by communicating more widely that further work and snagging would be required when the crossing opened.
“It should continue to keep the public updated of progress with this work.”
Auditor General Caroline Gardner praised the budgeting, governance, quality assurance and risk management which led to the scheme costing up to £245 million less than forecast when construction started in 2011.
She said it was too early to assess benefits such as cutting journey times, boosting economic growth and improving cross-Forth public transport via the Forth Road Bridge.
But a clearer plan should be produced as to how they would be measured.
Scottish Conservatives transport spokesman Jamie Greene praised the competitive bidding process for producing the best value for money.
But he added: “It unfortunately remains to be seen if this project, whilst magnificent in stature, will actually deliver any real benefits to commuters, businesses and local residents. Questions remain over the snagging works.”
Transport secretary Michael Matheson said there had been a “steady overall improvement” in journey times and there had been 14 occasions since opening when the bridge’s windshielding had averted traffic restrictions.
He said: “We aim to carry out a full post-project evaluation in late 2018, detailing performance relating to journey times and traffic flows.
“This will include an assessment of the impact of improved network connections and junctions, and the project’s contribution to economic growth and exploring what further support can be offered to public transport providers to meet any future increase in demand for travel across the Forth.”