What are common the obstacles faced by program managers in a multilingual environment?

Mainly communications problems besides some unexpected behaviours.

Information exchange

Communication is probably the main obstacle in a multilingual environment and can be tackled by the following means :

1) Divide the Program into a number of smaller projects/operations/activities and assign the team members with one language on each of these.  Assign one of the team members the role of interprator.

2) Have a Communications Management Plan that is formulated to reduce the communication barriers and is tailor-made to remove the obstacles posed by the multilingual environment.

3) Working with virtual teams located in different countries or regions through Video-conferencing using language translator techniques is another strategy under such situation.

4) Pairing of team members with one member knowing1 language and the other member knowing the foreign language alongwith the common language is another effective technique.

5) Depending upon the size and duration of the program/projects, it may also be feasible to train team members to learn new languages.

Since you mentioned "multilingual" .. this implies the possibility of "communication"problems , specifically miscommunication which leads to misuderstanding and possibly failures/conflicts in the work environment. This could also mean a "cultural" issue within the organization specially when these individuals speaking different languages have also different values, ethics ... The solution to this would be to use ONE standard language in formal business communication ... and to adopt ONE unifying corporate culture to be shared across all employees