They also have a bias from errors. Many articles have some fatal flaw that makes their results meaningless. If the distribution of errors is random, I think--though I'm not sure--that we should assume this bias causes regression towards an equal likelihood of positive and negative results.

I question this assumption. The distribution of errors that people will make in public communication tracks closely what they can expect to get away with doing. Errors (and non-errors, for that matter) that would result in social sanction will be reviewed more closely before publication, when they are generated at all. If your new satellite powered surveillance technique reports that the Emperor has No Clothes you double check.

The addition of 'noise' to a process with publication bias will enhance the strength of that bias. It also potentially increases regression towards equal negative/positive results. It is not clear which of these opposing influences will be stronger in a given field.