Associating CirrusSearch to allow others to find this task when searching in the corresponding project.

Yes this is a problem we identified, the completion suggester (responsible for autocomplete queries and the dropdown menu you are talking about) is able to detect a typo even in the 2nd character of the word while the algorithm responsible for the did you mean suggestion can only identify typos starting from the 3rd character.
This is inconsistent and we are trying to fix this problem by making the "did you mean" algorithm able to catch typos anywhere in the word.
The problem we have today is that we are not sure yet that this new technique is worth the effort, will it increase the number of false positives and make the "did you mean" suggestions even more annoying than what we serve today?

If you are curious to see how it would look like we have a test index available here: http://en-wp-bm25-inclinks-pv-reverse-relforge.wmflabs.org/w/index.php?title=Special:Search&profile=default&fulltext=Search&search=gound+plane

Note that the autocomplete suggestions are disabled on this test index.