The speech Marshall gives about the best burger is very similar in tone and speech pattern to Salieri's speech in Amadeus about Mozart's music.
During the flashback of when Marshall and Ted first move to NYC, and Marshall tells Ted how great cable TV is, there is a show of an "old Jewish lady wearing a bikini" he is likely referring to The Robin Byrd Show, a long running cable access show hosted by Robin Byrd, a former porn actress. She wears a bikini all the time.
Every burger bar the gang visit has a photo of Regis Philbin on the wall, usually behind the cast.
An ongoing joke from seasons 1-3 was that nobody ever found out what Barney's job was. Every time the gang would ask him he sarcastically replied, 'Please'! However, at the start of this fourth-season episode, it's revealed that Barney was involved in a hostile takeover of Goliath National Bank (GNB), and as a result of that, he shifted into management of the bank.