David Dimblebey hosted last night's unique edition of the show, whose audience was made up entirely of 16 and 17-year-olds who will have a vote in next year's referendum.
Members of the Radical Independence Campaign, whose members forced Mr Farage to cut short a recent visit to Edinburgh, last night waved placards in a protest outside the recording at the Corn Exchange.
Scottish Greens co-leader Patrick Harvie MSP made a formal complaint, saying the BBC is only interested in delivering "sensationalist confrontation" rather than serious debate on Scotland's future".
The LibDems described the BBC's line-up as "daft" and "puzzling" given it did not reflect political representation in Scotland.
The Electoral Reform Society in Scotland said the panel was more "pantomime than serious debate."
SNP MSP Jim Eadie has written to BBC director-general Tony Hall, seeking an explanation.
He said: "By adopting this one-sided approach, the BBC is failing its own traditions of high-quality public service broadcasting."
During the programme, SNP Westminster leader Angus Robertson protested at the panel's make-up, pointing to next week's by-election for the vacant Holyrood seat at Aberdeen Donside.
However, host David Dimbleby told him sharply that Question Time had never followed by-election timetables.
A BBC spokeswoman said it sought to provide as broad a range of political opinion as possible, while offering a UK-wide audience a varied and interesting political and current affairs debate.
The programme featured heated clashes between Mr Galloway, Mr Farage, and Mr Robertson over the nature and impact of nationalism.