Ed Crane says that human hair continues to grow after death. This is not actually true; since the skin dries out, shrinking and tightening around the hair follicles after death, this is in fact an optical illusion.
Ed Crane is approached to invest in a "new" technology/ business idea - dry cleaning. In fact, dry cleaning had been a flourishing business since the early 20th century, a key principle of the process having been discovered in the mid-19th century by a French inventor. A town as large as Santa Rosa CA (the setting) would certainly already have had 10 or more dry cleaners by 1949.
The train horn heard in the background is a diesel horn (air chime) from contemporary railroads. The Northwestern Pacific Railroad that runs through Santa Rosa would have still been using steam locomotives or early diesels so this should have been a steam whistle or the more melodious air chimes of the parent Southern Pacific Railroad.
Birdy Abundas says that Ludwig van Beethoven "was deaf when he wrote this. [...] He never actually heard it", referring to his Piano Sonata No. 8 in C Minor, Op. 13, "Pathetique". When Beethoven composed this specific Sonata in 1798, he wasn't deaf. He already had some auditory troubles but he became totally deaf later, around 1815. During the very beginning of the 19th century he was still able to play public concerts and to hear the pieces he was composing.
When Riedenschneider is talking to Ed in the jail after receiving information from the private detective: "You can't know the reality of what happened, or what would have happened if you hadn't stuck in your own Goddamn schnoz. So, there is no 'what happened.' Looking at something changes it. They call it The Uncertainty Principle. Sure it sounds screwy, but even Einstein says the guy is on to something." However, Albert Einstein never accepted Werner Heisenberg's uncertainty principle as a fundamental physical law, stating: "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced that He (God)does not throw dice." [Quantum Mechanics is based on laws of probability ... hence the reference to dice.]
When Doris is in jail and is talking to Ed across the table, when the camera is behind Ed's shoulder, smoke is billowing from the cigarette, but when the camera switches to the one behind Doris' shoulder, no smoke is coming from the cigarette.
When Ed lets himself in at Nirdlingers, he unlocks and opens the door on the right side. But when he leaves, he opens the door to the left. That door would have locks at the top and/or bottom that hold it closed even with the deadbolt unlocked and they can only be released from the inside (the order is you unlock the deadbolt, go inside and then release those locks so both doors swing free.) There would have been no reason for Ed to have unlocked those as well, since he wasn't opening the store for business, so that door should not have been able to be opened.
The goof items below may give away important plot points.
During the fight, there is a shot of Ed Crane's hands scrabbling on the desk for the cigar trimmer, but it slides out of his grasp. He shouldn't actually have it when he comes to stab Big Dave in the side of the neck.