Q:

Admit vs confess vs accept vs recognize vs avow

Are the following five verbs admit, confess, accept, recognize, and avow synonyms or we should be careful with the replacement of the verbs?
In which context can't I replace one of these verbs by another from these set?
For instance:

The company admits that there are some legal issues with its last patent.
The company confesses that there are some legal issues with its last patent.
The company accepts that there are some legal issues with its last patent.
The company recognizes that there are some legal issues with its last patent.
The company avows that there are some legal issues with its last patent.

A:

Particularly in the context of liability, some of these words can have significant legal weight as they can be a tacit admission of responsibility.  "Admit", "confess" and "accept" all often appear in statements that either acknowledge at least some degree of culpability, or deny any further culpability.  For example this is something you hear all the time:

The company has agreed to a settlement but admits no wrongdoing.

Similarly if you confess to something, or accept a decision, it means that you have agreed that you are at fault and are willing to pay the consequences.
In a legal context, "avow" is not much different from "confess", as it is equivalent to "swearing" or "taking an oath" and is a strong statement that can be used as evidence in court.

The defendant avowed that she'd never met the victim, a statement which was later used against her at trial to show that she had been deliberately misleading detectives about the truth of their relationship.

Finally, "recognize" is one of the words much-loved by lawyers, because it allows them to make a statement without saying anything significant.

The lawyer said that his client recognizes that there are legal issues with the patent, but feels these are not significant enough for a judge to rule against them in court.

Otherwise, depending on context, "admit" and "accept" can be substituted:

He admits / accepts there is some truth to the statement.

Although, bear in mind that the words mean different things.  "Admit" implies a verbal statement, while "accept" just indicates agreement.
Meanwhile "recognize" implies only perception, not agreement.
It's difficult to think of any situation where any of these can be replaced with either "confess" or "avow", at least not without making it a much stronger statement.  Also, "confess" and "avow" have a different action and purpose, so they can't normally replace each other.  A confession is an admission of guilt (or at least responsibility) while an avowal means you swear to the truth of something.

He confessed to the murder
He avowed that he killed the man, and he would do it again.

