OK, give me examples where a philosopher discovered a hole in a scientific argument that scientists missed. You can be trained in logic to perfection, yet without the domain knowledge you are unlikely to be able to spot any errors. Errors reducible to faulty syllogisms are rare in science.
Definitely, domain-specific knowledge is crucial; that's why I think it's in collaboration *with* scientists that philosophers can be most of use. Re your question, I think you overestimate humans in general! All of us are susceptible to believing/constructing flawed arguments ...
... (which are not the same as 'faulty syllogisms'), or purporting to 'prove' something that we actually haven't. Again, detecting this is not a skill unique to philosophers; I think here of how poor the connection between scientific hypothesis and statistical evidence can be in ...
... some published medical research. And obviously there are a lot of academic biostatisticians who do a lot of important work on that. From my inexpert perspective of someone who's studied a bunch of phil., and is currently studying mathematical statistics, I think phil. could add something here.
Dennett was a philosopher who studied and worked alongside scientists. He avoided ivory tower academic philosophical jargon - to his credit. He had (enough) domain knowledge to make an impact on science. Part of the problem I see with the present conversation is that you guys are talking about...
philosophers and scientists as if they were people in two different departments wearing badges that say "philosopher" or "scientist". Academia loves its silos. The real breakthroughs usually happen in the margins.