I remember the day I learned that Python's "re" module uses backtracking for non-extended regexes. My tests covered lots of corner cases in the regex logic, but were too short for me to notice the performance penalty. Luckily I only caused a partial outage in production.
I actually got to talk to Raymond Hettinger (Python core team) about why re uses a potentially exponential-time algorithm for regexes when there is a famous linear-time algorithm, and (I suspect) most programmers would assume linear complexity. As it turns out, there was an attempt to re-write re to fix this, but the re-write never managed to present exactly the same (extremely large) API as the existing module. He advised me that "the standard library is where code goes to die."