When "typing up" a handwritten record, your rendering of it should be as true to the original as possible, not a "cleaned up, I know how to spell everything correctly" version. Transcribing a document is not the same as editing or correcting it.
The reasons for not making changes are pretty simple. What the transcriber thinks is wrong may not be wrong. "Incorrect" spellings may be clues as to how names were actually pronounced. And there can always be other clues in what originally appear to be "errors."
Annotations to the transcription can be made. Comments regarding "errors" should be made inside brackets [ and ], so that it's clear where the comments begin and the comments end.