For Apollo, it wasn't so much a "mistake" as a conscious decision to save weight. The Gemini IMU used 4 gimbals, and so avoided the issue entirely. Apollo dropped the weight of the extra gimbal and instead required the pilots to avoid flying in certain orientations.

I would characterize this more as a hardware engineering choice, with associated work around in software (don't rotate the spacecraft through gimbal lock/Euler angle singularity).

Disclaimer: IANARS

Yes large differences in orientation will make Euler angles gimbal lock. And it looks strange, even for small differences in orientation.

https://www.youtube.com/watch?v=Ocoibc7MoKg

The Shuttle program used quaternions, although the ISS apparently uses a definition that is easier to read by sight: http://webcache.googleusercontent.com/search?q=cache:-ivJED8...