The current implementation assumes that when running in mongos it should be merging results from the shards. While this applies to the first $group, it doesn't apply to any others.

mongos> for (var i=0; i<100;i++) db.foo.insert({_id:i, i:i%10})
mongos> db.foo.aggregate({$group:{_id:'$_id', i:{$first:'$i'}}},{$group:{_id:'$_id', i:{$avg:'$i'}}})
{
	"errmsg" : "exception: assertion src/mongo/db/pipeline/accumulator_avg.cpp:43",
	"code" : 0,
	"ok" : 0
}

Note that both stages in the pipeline work by themselves and should return each document unmodified. Also, the combined aggregation works when running on a single server.