Peer review is important for checking the correctness of the results, among other things. It's not uncommon to find big errors; small mistakes are everywhere.
Peer review is of utmost importance. Any researcher can make mistakes. I can read papers and apply them, but I need expert opinion to trust the papers. I am not skilled enough in any but my specialties.
I do see papers with outlandish claims and very weak support. This kind of excessively bold statement I see in many papers is a red flag for me.