The presenter also spoke out against its "closed corporate culture" and said recent revelations about excessive pay-offs for executives and the millions wasted on a failed IT project had tested "the public's patience".
Among the payouts that sparked a recent storm of criticism were £470,000 to former director-general George Entwistle after only 54 days in the job and £680,000 to former chief operating officer Caroline Thomson.
Deputy director-general Mark Byford departed the BBC with a total payout of £949,000.
Only last week, an influential committee of MPs said the BBC was "far too complacent" in its handling of the Digital Media Initiative (DMI) which was scrapped at the cost of almost £100 million of licence fee-payers' money.
Paxman said: "It is smug. I love the BBC in many ways, but at the same time it has made me loathe aspects of it, and that's a very odd state of affairs.
"When I see people being given £1 million merely for walking out of the door, when I see £100 million being blown on that DMI [digital media initiative] thing, a stupid technical initiative like that, I start wondering: how much longer are we going to test the public's patience?"
He also said the BBC had "an unfortunate history" of expanding into areas including online news and "extra" television and radio channels.
He said: "The great smell that comes off those pay-off scandals - and I think they are scandals - is of an organisation which became complacent, preoccupied with the conditions of its senior staff, at the expense of a strategic vision."