We were doing fine until the last four questions, the first of which led to contentiousness and recriminations and eventual apologies.  If it wasn't phrased more craftily than below, there are two possible answers.  We missed all of these:

How many levels are in Maslow's hierarchy of needs ?

Who was the longest-serving U.S. Supreme Court justice ?

What English name, possibly deriving from the Hebrew for "to behold", was the first-or second-most popular female baby name in the United States from 1981 to 1998 ?

What U.S. president was featured on a $5000 bill ?

What is the oldest U.S. military award?

Who were Arabella and Anita, whose zero-gravity skills were tested on Skylab in 1973?

What American fashion designer, born in 1942, is known for closing her shows with a cartwheel ending in a split?

Who was the first American to win a Nobel Peace Prize, for mediating the end of a war between two nations?

What Madrid museum displays The Surrender of Breda by Velazquez and The Third of May 1808 by Goya?

What one-word title is shared by Justin Timberlake's debut solo album and a 2010 neo-western crime drama series on FX?

What nine-letter word describes one of several forms of the same chemical element, such as diamond, graphite, or buckminsterfullerene ?

In what countries are the following four-letter cities:  Lima, Giza, Cork, Cebu, Kano ?
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What composer's last opera was The Magic Flute ?

I resisted trying Nethack 5.0 for a while, but there is some good news:

"You finish eating the xorn corpse.  You feel less concerned about becoming petrified."

There's also a tutorial mode which should help anyone who wants to start playing Nethack after 40+ years of development.

What vitamin group, which includes retinol, is important for healthy vision?

What Basque sport is similar to racquetball and squash?

Shopska salad is the national dish of what country?

What island nation was the setting for Dr. No?

What Dr. Quinn actress starred in Live and Let Die?  

What make of car replaces Bond's Aston Martin in Tomorrow Never Dies?

What is the logo of SPECTRE ("Special Executive for Counter-intelligence, Terrorism, Revenge and Extortion")?

Who sang the first Bond film theme song to win an Academy Award for Best Original Song?

What 2011 Martin Scorcese film with a one-word title starred Asa Butterfield, Ben Kingsley, and Sacha Baron Cohen?

The Battle of Tewkesbury was a decisive event in what conflict?

What influential video game trilogy by FromSoftware is noted for its extreme level of difficulty and a subgenre which it inspired?

The four major networks haven't been nominated for an Outstanding Drama Series Emmy since what CBS legal drama in 2011?

We were in third place before the final question, but won thanks to our team members with midwestern roots!

The official sports of Canada are ice hockey and what summer sport?

The oldest MLB rookie was what Negro Leagues star who signed with the Cleveland Indians on his 42nd birthday?

What U.S. president campaigned with the slogans "Vote Yourself a Farm" and "Don't Change Horses in Midstream"?

What mother of one of Henry VIII's wives was the first real woman to be depicted on a U.S. coin?

Lake St. Clair, with an average depth of 11 feet, connects which two Great Lakes?

Our go-to restaurant for trivia unexpectedly canceled their contract in the middle of the season.  Too few customers?  I'm guessing attendance falls further on that night.  So we went elsewhere and triumphed over a much larger crowd!

What city has the oldest subway system in the USA?

What scale is used to measure the spiciness of peppers?

Who fought Muhammad Ali at the Thrilla In Manila?

What country has the most combined men's and women's World Cup championships?

London Bridge was disassembled and moved to Lake Havasu​​​​​​​ in what US state?

What American comptitive eater has won the Mustard Yellow Belt a record 17 times?

What sort of fully-functioning object was "America", a 227-pound 18-karat gold artwork that was exhibited at the Guggenheim Museum and then stolen from Blenheim Palace?

What American company (the world's first billion-dollar corporation) was co-founded in 1901 by Elbert Henry Gary, for whom Gary, Indiana was named?

What did Gertrude Ederle become the first woman to swim across?

Who was Emperor of Japan from 1926 to 1989?

What was Ernest Hemingway's debut novel?