Brooks was already uncomfortable directing a script he hadn't conceived himself, having only taken Blazing Saddles because he was flat broke after his first two movies had bombed, and only agreed on the condition that he would co-write the screenplay with Wilder. Wilder, in turn, told Brooks that he couldn't appear on screen so as not to disturb the Comically Serious atmosphere. Brooks only did a handful of voice-overs: he's the werewolf howl ("There wolf! There castle!"), the elder Dr. Frankenstein and the screaming cat who gets hit by Fredrick's dart.
Brooks repeatedly questioned Wilder's insistence to include the now-famous "Puttin' On The Ritz" and attempted several times to talk him into cutting it. Wilder persisted until he was blue in the face just to convince Brooks how badly he wanted it, to which Brooks finally said "If you feel that strongly about it, we'll shoot the scene. If it works, we'll use it, if not, we won't." He still wasn't convinced come shooting until he turned to see the entire crew covering their mouths with handkerchiefs (which he'd told them to do if they started laughing), at which point he knew that it would be a hit.
Throughout the shoot, Brooks and Wilder continued to argue over direction. At one point it got so bad that Brooks stormed off the set one evening, later calling Wilder that night to apologize in his own way by asking "Who was that asshole you were fighting with today? If you ask me, he should be fired!"
In the end, both men agreed that dealing with these creative differences were not worth risking their friendship and that it was probably best that this be their last project in cooperation with each other. Wilder was increasingly drawn to screenwriting and Brooks only wanted to direct his own scripts at this point, encouraging Wilder to direct his own (Brooks later offered Wilder the lead in High Anxiety, which he felt would have been perfect casting, but Wilder turned down due to scheduling issues). Young Frankenstein is generally seen as both men's peak period, as none of their other projects, despite being well-received, reached anywhere near the same acclaim, although true to their words they remained best friends until Wilder's death in 2016.
Deleted Role: Leon Askin played a lawyer (reading the last will) but was cut out.
Igor's hump, which changes position from scene to scene; Marty Feldman decided to do this on his own, without telling anybody beforehand. When someone finally noticed, they added a bit where Frederick does as well.
During a search in the forest, Inspector Kemp's wooden arm appears to have switched sides. On closer inspection, it's actually the entire scene that's obviously been flipped as his eyepatch and monocle are on the other eye, and his badge is on the other side.
Mel Brooks ad-libbed the sound of a cat getting hit with one of Frederick's darts.
The monster's shout of "PUTTINAHNDARIZZZ!" was Peter Boyle's idea.
"Soitenly! You take the blond, I'll take the one in the toiban!" Marty Feldman's Groucho Marx-esque riff was one of many moments that Mel Brooks was not expecting, to his delight. Of course as the Hilarious Outtakes show, just because they left it in didn't meant it was easy to shoot (mostly because everyone was laughing so hard).
The blind man's parting line "I was going to make espresso!" was improvised by Gene Hackman. The scene immediately fades to black to cover up the laughter of the film crew.
Wilder wrote in his autobiography that he kept trying to find ways to add additional scenes to the shooting schedule because the cast had a thoroughly great time together and Wilder didn't want filming to end.
Originally in the script, after Igor drops the brain jar, he was to turn to the camera and quip, "Funny thing is, I tried!"
The "Puttin' on the Ritz" number almost didn't make it into the film. Wilder fought tooth and nail with Brooks to include it until the latter relented and allowed it to be filmed. Even then Brooks figured he'd just delete the scene anyway before he watched back the sequence and realized that it totally worked.