What do you call the the effect that causes people to miss the "the the" in this title?

This is referred to here and numerous other places as "top-down vs. bottom-up" processing, and is a cognitive error rather than a visual one - that is, the illusion is caused by filtering of the material seen to match expectations as opposed to a true visual illusion, which exploits faulty visual processing.

The original illusion is stronger than it is in the title here because the phrase is broken across lines:

PARIS IN THE
 THE SPRING

On a quick glance, the "top-down" processing matches the sentence against similar phrases familiar to the reader, and results in a match to "PARIS IN THE SPRING", and the perception that this is what is there. In contrast, if the reader specifically reads each word separately -- "bottom-up" processing -- they look at one word at a time, and see

PARIS    IN    THE    THE    SPRING

thereby detecting the duplicate "THE".

It's probably reasonable to to say that it is a facet of inattention blindness.

It's a factor of how our minds filter stimuli for consumption.

I don't know if there is a more specific term that applies.