Interesting algorithms in the formalization of the Feit-Thompson theorem?
(Turning a comment into an answer, and expanding on it)

From talking to someone who worked on this: no. He invented all sorts of clever refinements to many proofs, and restructured many theory developments, both of which are extremely valuable, but the algorithms involved are not interesting -- in fact, many of them are dumb brute force, the very opposite of interesting.

Basically what was sought was as direct a line to the proof of Feit Thompson, without worrying about 'computational content' along the way (and even not overly worrying about reusability of some of the modules).  This was already extremely ambitious given the timelines.  Luckily, several of the people involved in the project have gone on to refactor many parts of the proofs to be


more reusable for a wider set of applications
more computationally meaningful