(2-part post):
The first thing that the consular officer will have to establish is whether your partner has committed ANY offence of 'moral turpitude' after reaching the age of 18. If he has, he's automatically ineligible (in the first instance) for a US visa. The consular officer has absolutely no discretion in the matter. The US Immigration and Nationality Act applies and the US embassy MUST refuse to issue a visa. However the applicant can then apply for a 'waiver of ineligibility', but that application has to be considered in Washington. If a waiver is granted, the visa application can then be reconsidered (but there's still no guarantee that a visa will be granted).
Whether 'GBH' falls into the definition of 'moral turpitude' probably depends upon the circumstances. If it was "with intent to commit serious bodily harm" or "with a dangerous or deadly weapon" it definitely does. Otherwise it probably doesn't:
However the 'other small things' you mention might (if they were committed after the age of 18) be far more serious. All theft constitutes 'moral turpitude'. So, as far as the US authorities are concerned, nicking a Mars bar is worse than committing a serious assault. Fraud (e.g. using a child ticket for adult travel on the Underground) also counts as 'moral turpitude':
http://www.state.gov/...rganization/86942.pdf