E.g. a miner submits a valid PoW for their block but rewards herself 25 BTC instead of 12.5. Does that miner get a chance to fix her mistake?
If they reward themselves an invalid amount of Bitcoins, then it's not a valid proof of work, because it does not satisfy the conditions that are agreed. In your case, if a miner chose to reward himself 25 BTC instead of 12.5, he'd have to redo the proof of work in order for the block to be considered valid.
Doesn't matter if it's 1 Bitcoin more or even 1 satoshi less, if it's not precisely what it needs to be, such block is invalid.
Actually, it can be less than the standard block reward. One could simply choose to be rewarded with 5.25 BTC and bring that 1 BTC out of circulation. It's their decision as it's their money; it really doesn't differ much from the
OP_RETURN.
For more information:
https://bitcointalk.org/index.php?topic=5342114.msg57215743#msg57215743