It is not rare for math papers to have minor issues. Referees do the best job they can, but their job is not to find every minor issue - the author should ideally do that. Papers are written by humans, in any case, so perfection is rarely achieved.
This doesn't have as much impact as you might think because people don't blindly cite proofs from other papers. If a paper proves an important result, which others are planning to rely on, the others will check the proof to their own satisfaction. Refereeing does catch many errors, but nobody relies on refereeing alone for important results.
Another reason that minor errors might be overlooked is that, apart from perhaps the referee, working mathematicians who read a proof often read it just to get the main idea, and then re-work the proof in their own head, rather than following along with the author's description of the proof. For experienced mathematicians, that's often more efficient than trying to work out the details of what the author is saying. Only when the mathematicans can't work out the proof on their own do they need to try to decipher the author's detailed argument.
That's very different from how students (undergraduate and graduate) read papers. Students often have less experience with the "standard" techniques, and need more than just a hint about how to prove a theorem. So students often need to read the full proofs. When doing so, take note of which ones you think are clear, and which you think are not, and try to emulate the clear ones in your own writing.
