You are directly hitting one of the current limitations of MongoDB.
The problem is that the engine does not support several positional operators.
See this Multiple use of the positional `$` operator to update nested arrays
There is an open ticket for this: https://jira.mongodb.org/browse/SERVER-831 (mentioned also there)
You can also read this one on how to change your data model: Updating nested arrays in mongodb
If it is feasible for you, you can do:
db.collection.update({_id:2,"event_type.name":'MT' ,"event_type.language.name":'English'},{$set:{"event_type.0.language.$.count":<number>}})
db.collection.update({_id:2,"event_type.name":'MT' ,"event_type.language.name":'English'},{$set:{"event_type.$.language.0.count":<number>}})
But you cannot do:
db.collection.update({_id:2,"event_type.name":'MT' ,"event_type.language.name":'English'},{$set:{"event_type.$.language.$.count":<number>}})