A large element of the plot in the episode centers around the illegality of Archer having sexual relations with a 16 year old girl. This is, however, not illegal in Switzerland (or anywhere in Europe other than Turkey and Malta), where the age of consent is 16; though it might still be considered taboo by many, given the age cap, it is not something Archer could find himself in legal trouble for.
In the Videotex ad shown by Ms. Archer during the briefing, it says, "Ihr Traum, Mein Realität". The correct German is "meine Realität".
Archer refers to a case of severe frostbite as "first degree". It is likely that he actually meant "third degree", which is the most severe type of burn. Burns are backwards from law violations.