Handling errors: If you make a mistake in your logbook (and you will at some point), simply draw one line through the mistake so it is clear to the reader what adjustment was made. No scribbling. No white-out.
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61.59: “Falsification, reproduction, or alteration of applications, certificates, logbooks, reports, or records.” In a nutshell, no person can make or cause to be made a fraudulent or intentionally false logbook entry, and violations can lead to suspension or revocation of an airman certificate, rating or authorization ...
A pilot is actually only required to log that time necessary to demonstrate currency, or to document the requisite experience necessary for a certificate, rating or flight review. However, for insurance purposes it is likely advisable to log all time. § 61.51 Pilot logbooks.
The FAA doesn't lay out exactly how you should log your hours, even those hours that the rules require. While commercially available paper pilot logbooks have been the standard for decades, nothing specifically says a digital one won't do.