Please, consider the following use case:
> use foo
switched to db foo
> db.test.insert({ Article : "Bla-bla", TagDesc : [

{Name : "Nature", Rate: 10}

,

{Name: "Culture", Rate : 2 }

] })
> db.runCommand({ findandmodify : "test", query :

{ Article : "Bla-bla", "TagDesc.Rate" : 2 }

, update : { $set :

{ "TagDesc.$.Name" : "Economics" }

} })
{
"value" : {
"_id" : ObjectId("4bda64d1967d194e851b03ed"),
"Article" : "Bla-bla",
"TagDesc" : [

{ "Name" : "Nature", "Rate" : 10 }

,

{ "Name" : "Culture", "Rate" : 2 }

]
},
"ok" : 1
}

server console output:
Fri Apr 30 08:07:36 foo.$cmd Caught Assertion in update , continuing
Fri Apr 30 08:07:36 update foo.test query:

{ _id: ObjId(4bda64d1967d194e851b03ed) }

exception userassert:can't append to array using string field name 0ms

The object was not changed
> db.test.find()
{ "_id" : ObjectId("4bda64d1967d194e851b03ed"), "Article" : "Bla-bla", "TagDesc" : [

{ "Name" : "Nature", "Rate" : 10 }

,

{ "Name" : "Culture", "Rate" : 2 }

] }
>

Note that at this time we specified index of item manually instead of using positional operator ( "TagDesc.$.Name" -> "TagDesc.1.Name" ).
And changes were applied successfully.
> db.runCommand({ findandmodify : "test", query :

{ Article : "Bla-bla", "TagDesc.Rate" : 2 }

, update : { $set :

{ "TagDesc.1.Name" : "Economics" }

} })
{
"value" : {
"_id" : ObjectId("4bda64d1967d194e851b03ed"),
"Article" : "Bla-bla",
"TagDesc" : [

{ "Name" : "Nature", "Rate" : 10 }

,

{ "Name" : "Culture", "Rate" : 2 }

]
},
"ok" : 1
}
> db.test.find()
{ "Article" : "Bla-bla", "TagDesc" : [

{ "Name" : "Nature", "Rate" : 10 }

,

{ "Name" : "Economics", "Rate" : 2 }

], "_id" : ObjectId("4bda64d1967d194e851b03ed") }
>