Harold rips his necktie in half after getting it caught in the sewing machine, but then in scenes immediately following, his tie is whole again.
When Harold imagines his encounter with his "Vampire", he ticks off the experience in a memorandum book on the verso side, the recto side of which lists the month as October. When he imagines his subsequent encounter with his "Flapper", he ticks off that experience beneath the previous one, only the recto side of the book now reads as April.
When Harold helps Mary out of the boat, the lilting boat is causing a lot of ripples in the water behind them. In the very next shot, the water has become still again, with none of the wake from before.
Harold only tears the publisher's envelope into a few good-sized pieces, yet the check inside is shown as having been torn into many small pieces.
When Harold is trying to not sit next to Mary on the train, it is shown going around a sharp right curve, and he should have been thrown to the left side of the car, not right towards Mary as seen in the film.
Harold rips the publisher's envelope into small pieces (and indeed, he tears it into such tiny shreds that the check inside is torn into four narrow strips at one corner, so that the digits of the "3000" are separated into individual shards of paper), yet the cover letter stating, "Dear Sir, We have decided to publish your manuscript as a humorous work and have renamed it 'The Boob's Diary'. We think it's very funny. Enclosed is a check for $3000 in advance royalty payment" is mostly undamaged, with just a single straight tear across the middle of the sheet. If a sealed envelope is torn up into that many pieces, then the entire contents will be shredded, also --- one enclosure would not get torn up finely, and yet another paper be able to escape with just being torn in half.
In the principal of "united we stand" (as is so eloquently illustrated with the bundle of sticks in "The Straight Story"), a thick sheaf of paper sheets is hard to rip through all at once, so it would be impossible to tear up several layers of folded paper into narrow strips, the way Harold supposedly does with the check when he tears up the sealed envelope without opening it. To actually tear the check between each of the digits of the "3000" so that it formed four individual narrow strips, Harold would have needed to remove the check from the envelope, and also separate it from the cover letter, so that he could have just the single fragile sheet to minutely tear into the thin shards.
When Harold disconnects the moving tram from the overhead electric wire, it doesn't just roll to a halt and isn't on a hill; it keeps going at normal speed.
Harold has to turn to his right to drive down the rutted detour route, yet when he re-enters the highway a minute later, the alternate route's exit is on his left, not his right. Obviously, it is just a second shot of the same detour-entrance with its long line of traffic barriers, filmed from the opposite direction.
Harold's car bounces up and down on the dirt road. It continues to bounce when he turns on to a flat, paved road. In a brief shot of the driver's side of the car, the rear wheel is inadvertently revealed to have an off-center hub, thus causing the car to bounce on the flat road surface. The trick wheel was used for the special effect, and wasn't meant to be noticed. Had it been intended as part of a joke about the car being damaged, it would have been featured in a close-up shot.
When Mary's car goes off the road and in a close shot she takes out the Cracker Jack box, there is a reflection in the side of the car (bottom left) of a pair of legs standing nearby, then walking away.
As Harold is carrying Mary off, Uncle Jerry and Ronald DeVore's wife show up outside the Buckingham Estate in a car which Uncle Jerry is driving, so evidently this vehicle was owned by Uncle Jerry, and thus Harold would almost certainly have been aware that his uncle had it. So both Harold and Uncle Jerry would have also known that they would not have needed to make the dash to the train station, nor would Harold have needed to make the perilous multiple-conveyance journey all the way from Little Bend to Los Angeles; the three of them could have just gone in Uncle Jerry's car just as soon as Ronald's wife identified herself to them, and arrived at the estate with time to spare.
Even though the phone-operator invalidly disconnected the pay-phone at the Little Bend train station, Harold's dash all the way from there to Mary's home in L.A. still wouldn't have been necessary; Harold could have just travelled far enough to find another phone and call the estate from there to tell them about Ronald's wife, and then Mary's family would have simply postponed the wedding till Harold got there with the locket as proof that Ronald was already married.