I sent a check to my credit card company for $1234. The automatic check reader there read it incorrectly as $12.34, which was the amount that was paid and also what was cleared from my bank. I looked at the image of the check and my handwriting was fine, so I am curious how often this happens. I've never heard of it before, and I can't find any account of this happening online.
Your question was,
I am curious how often this happens
The short answer is, not very often at all. Infrequently enough that many people will never experience it and may not even know someone who has experienced it. I will include some rough numbers below, based on my personal experience working in the financial industry - I'm not aware of any publicly available data that's pooled across the industry as a whole.
As you seem to be aware, checks are essentially processed based on a scanned image. Financial institutions use check processing machines and software to process the images. Essentially, the paper document is digitized and OCR (optical character recognition) is applied, which translates the image into numbers.
A key point is that the process is semi-automated - the OCR process has accuracy rules that essentially assign a reliability score to the image as it is processed. Images with high scores (that is, images which the system is fairly certain it has guessed correctly) are typically submitted automatically, without human intervention (at least in terms of validating that the data matches the image).
On the other hand, images that are processed under a certain score (i.e. the system is unsure if it guessed correctly or not) are stopped and queued for a human to verify. This threshold is often set very conservatively, in order to ensure accuracy (it's cheaper to get a human to click through verification on a handful of images in order to catch the actual errors, than it is to deal with an angry customer because of bad data).
Verification queue rates for the OCR process can be as high as 30% - that is, the system is asking a human to verify the lowest-quality 30% of the data it processes. But, it's only actually wrong maybe 1 - 2% of the time. When you add human verification to the OCR process, the error rate drops very quickly. While errors do happen, as you experienced, error rates are typically incredibly low - an institution processing 5,000 paper checks per day may only have 1 actual encoding error per day, which works out to around 0.02% - and a portion of those errors are caught by the FI(s) handling the check and/or the Fed; many times the end customer doesn't even realize there was a mistake.
In other words, you could reasonably expect to write a check every day for the next 13 or 14 years before you saw another error. Considering that even a prolific check writing individual might only average a dozen or two checks per month, most people will never experience an encoding error like you have.