Establishing common ground is critical in intercultural communication. Still, little is known as for the practice of common ground in machine-translation mediated communication. In this paper, we report some of the critical communication difficulties related to common ground when intercultural communication is mediated by multilingual collaboration systems. Based on empirical investigation of the communication between Japanese and Danish students applying a multilingual communication system, we identify two main challenges influencing common ground: 1) Difficulties in exchanging socio-emotional aspects and 2) Difficulties in developing shared concepts. As theoretical constructs, social context and project jargon, which are known as essential contributors to the construction and the maintenance of common ground, are harnessed to explain such difficulties.