Contrary to Javi's statements, "international banking regulations" are VERY strict, post-9/11, with additional regulations pertinent to Swiss banks coming in force prior to this episode's air date. There certainly should be ways to discover where that much money came from and where it went. International wires of any reasonable size (certainly one for the amount noted in the show) require a good deal of documentation and verification, all of which must be maintained for a number of years. In addition, even numbered accounts require personal information to be opened, and such information can be accessed by law enforcement with appropriate warrants.
Beckett and Castle making their wedding list at the end makes no sense. They make the stipulation to only put people on their individual lists that would need to be there to make them happy. Alexis and probably Martha should be on Castle's list, and Beckett's father and probably Esposito and Ryan would be on Kate's, yet they both only write 'you,' on their lists. Castle then says he needs to invite his mother, and Alexis, almost as an afterthought. Kate says the people at the precinct, but all of these people would have been on their actual lists to begin with.
Discussing sensitive financial matters is not insider trading. Trading (or soliciting a trade, or preventing a trade that would have happened without such knowledge) *based on inside information* is insider trading. Merely knowing the information isn't against the law and neither is spreading it; acting on such information is. (There is also legal insider trading - trading by insiders with proper permission and documentation - but most people not in the industry don't pay attention to that.)