[Butch Cassidy Slept Here]

Unfortunately, it looks like you don't have anything in writing you could use against Continental in Small Claims Court. Even if you provided Continental with an e-mail contact they, obviously, are not going to incriminate themselves in writing.

New Jersey is one of the states that allow recording of phone calls. Only one party to the call need be aware the call is being recording, and that one party can be yourself, again, as long as you're participating in the conversation. The point is Courts, sometimes, will allow recordings to be admitted as evidence. So, recordings of any calls placed from within New Jersey MIGHT be admitted as evidence in a New Jersey Small Claims Court. Continental, or any other major US airline, would be hard-pressed to object since they record calls on their end.

Unless you're willing to endure multiple connections Continental is the lesser of two evils to Port of Spain. The other option is American Air, and they can make any problems you've had with Continental look like nothing.