I'm referring to the waiter who appears in the scene where the judges are talking to the reporter in the restaurant, and says "May I take your orders, please?"
The grin and the crazy hair remind me of the late Lloyd Bridges character from the movie Airplane, "I guess I chose the wrong day to stop sniffing glue."
The OP is referring to Norbert Schiller who has a tiny role as a waiter in a café/night club that Judge Haywood (Spencer Tracy) visits after being invited to dinner by Judge Curtiss Ives (Ray Teal) with Mrs Ives (Sheila Bromley). Judge Ives spots the reporter Max Perkins (Bernard Kates) who is accompanied by Mrs Bertholt (Marlene Dietrich).
This scene immediately follows the strong and harrowing one of the testimony from Rudolph Petersen (Montgomery Clift). I believe it is intended as a lighter scene after the gripping performance by Clift and has some nice banter between the judges about political affiliations and some humour with Judge Haywood again struggling with unusual and unfamiliar German words, such as the wine Schwalbenwinkel suggested by Mrs Bertholt. As the scene is designed to be more light-hearted the slight comic performance of the waiter is entirely appropriate.
I think the OP is having a lend of us by suggesting this is "a ridiculous moment" in the film. Schiller only has three lines and it is almost a blink and you miss it performance. I think the OP is just wanting to point out that they thought Schiller looked comic and a little bit like Lloyd Bridges.
stevekaczynski is correct stating that Schiller also had a minor role in "Young Frankenstein" (1974) - again uncredited. A funny little turn as the master of ceremonies introducing Dr Frankenstein's performance with 'The Creature' which ends with a hilarious 'Puttin' on the Ritz' routine.
Actually I remember Schiller more in another tiny role but in a film also about Nazi War Crimes Trials and again starring Maximilian Schell, this time as the accused. I can recommend this film, "The Man in the Glass Booth" (1975), which has a key scene with Schell's character succinctly, emotively and extremely effectively, outlining from the dock the reasons for Hitler's rise and why the German people continued to support his evil and insane regime. The scene in "The Man in the Glass Booth" is indeed very similar to the climatic moment in "Judgement at Nuremberg" when Ernst Janning (Burt Lancaster) makes his statement to the court but I feel Schell's performance, and the writing in "The Man in the Glass Booth", is far better. In another scene in "The Man in the Glass Booth" Schell compellingly and shockingly describes the unimaginable practices of Einsatzgruppen units. His role is so chilling in "The Man in the Glass Booth" as he also has great charm and even humour. I would highly recommend the latter film to those interested in this subject.
"Judgement at Nuremberg" used a lot of German and Austrian actors who had escaped to the US before WWII and found work in American TV and films. Schiller, like Schell, was Viennese. To go further on this tangent, there is another Austro-Hungarian born actor in "Judgement at Nuremberg" who plays a tiny uncredited role as a waiter for slight comic relief. This is Oscar Beregi Jr as a waiter, presumably in a café area within the Palace of Justice, who approaches Judge Haywood (Spencer Tracy), Senator Burkette (Edward Binns) and Judge Ives (Ray Teal) when they are discussing the implications of the upcoming verdict in the light of the Berlin Airlift (it is the scene just before Janning's court testimony). Again it is a moment of slight comic relief with the waiter using a 'strange' German word which perhaps sounds amusing to American ears and the waiter's line of "more strudel, gentlemen?" is something of a mundane non sequitur after the discussion of high political affairs.
Beregi, like Schiller, was born in the Austrian-Hungarian Empire before the end of World War I and left Europe before WWII for the Americas eventually finding roles in American TV and film (both Schiller and Beregi even had a few roles in Hogan's Heroes famously starring Werner Klemperer who plays Emil Hahn in "Judgement in Nuremberg"). Beregi too had a small role in "Young Frankenstein" as the gaoler threatening 'The Monster' (Peter Boyle) who had been arrested after the disastrous ending to the Puttin' on the Ritz routine. Indeed, going further down the rabbit hole, Beregi (although HE looks nothing like him) has also starred alongside Lloyd Bridges in Sea Hunt (1958) and the Lloyd Bridges Show (1963)!
A fairly common narrative technique is to introduce the occasional comic moment into general tragic material. Shakespeare does this in Macbeth, where, just about the time Macbeth is murdering Duncan, there is a scene with the castle porter, who among other things talks about the effect of alcohol on sexual performance.