I am presently in a dispute with a US-based computer company over abusive charges they want me to pay for a very basic service. As I am not sure the dispute will be resolved before I travel to the US (no criminal charges have been filed as the amount is quite small, USD 1,200.00). Could this prevent me from traveling by air to a vacation in the US?
Personal service of court papers could be made while you're in the USA. However, doing so successfully would require the opposing party to know where you'd be at a particular time, and then to physically find you at that place and time, and then to approach you with the documents.
It's a big country. It's not clear that the opposing party would have any of that information, or be able to execute on it.
Further, I've never heard of the US immigration authorities involving themselves in civil law disputes of any kind, or even asking about them. None of their paperwork asks about this sort of thing, and a visitor needn't (and shouldn't) volunteer the info.
Source: I'm a lawyer.